## Monday, May 28, 2018

### One Way to Run an Economy

There is more than one way to run an economy. Today, let's explore a single way.

In our imagination, we have an isolated island with it's own currency. With sunny days and pristine beaches, they wish to join the wider world's economy.

They collectively decide to advertise their island, offering a one week stay for XX.XX in their currency or YY.YY in a number of other currencies. It seems to me that they are setting their own foreign exchange rate. They would need to decide among themselves how the divide the cost of providing that one week experience.

OK. With a plan in place, they begin the experiment. After one year, they find that they have a booming business. They have more people arriving than they can handle. What do they do? Change the exchange rate? Put people on a waiting list? Send guest home dissatisfied?

Whoa. We have too many possible answers! We need to more accurately examine how this island's business is economically arranged. Let's assume that government has been issuing local currency in exchange for foreign currency. This local currency has been obtained from a stable system of taxation that results in an agreeable balance within the island's economy.

Returning to the problem of excessive success, the island government decides to decrease the exchange rate, which results in a decrease in the amount of local currency for each unit of foreign currency. In other words, the price of a week on the island has increased in terms of foreign currency. This action stabilizes the tourist industry but leaves it running at a high and nationally profitable level.

Let's continue this story for 50 years. Our island has a stable, successful tourist industry. Government routinely spends part of the foreign currency and saves part in the form of bank deposits and safe investments in the currency of foreign origin. After 50 years, large sums of reserves are held in some nations.

Could this really happen? Think China? Think Japan? "Whoa!" someone shouts! "Those are both exporting nations. Just the opposite of this story." Hold that thought until later in the article.

Now we add a new twist to the story. An enterprising journalist (who is also an amateur economist) notices the large sums held by a single nation. He also notices the large number of tourist on vacation. He writes a story. The story is read by a politician. We have a political moment.

The story expresses concern about the large overhang of potential spending by this single island economy. There is concern that people are off vacationing rather than working, which just continues the trend long in place. Something must be wrong, but an exact problem and suggested solutions are not part of the article.

Eager politicians begin blaming this island nation for causing unemployment in other nations by failing to spend all of it's earnings (Like the critics were doing?).  Politicians begin expanding the argument by complained that vacations spent on the island could have been provided in-nation to reduce the unemployment numbers and improve the balance of payments. Obviously, according to some politicians, the island nation was doing some things wrong. Maybe the exchange rate was not correct.

This seems to be a good place for ending the story. The political story has developed into something that we can learn from. A single government is controlling the exchange rate. The method of money exchange allows the controlling government to claim a repeated annual share from the labor and resources provided by the entire economy. The situation has gone on long enough to attract the attention of media and political elements.

Except for the critics, everyone seems happy with the stable economy described. Is there REALLY a need for change?

I would suggest that need for change is in the eye of the beholders. The island described is neither China nor Japan, but the effects on reserves and unemployment can be made to sound the same. Every national economy has the ability to arrange a division of resources within it's borders. Whatever arrangement is made has potential interactions with other national economies, which will be developed if mutual benefits for each side can be found.

The economies and economic interactions we have in today's world are the result of political and individual decisions on thousands, maybe even billions, of levels. The illustration provided in this article is just one way to run an economy.

## Sunday, May 6, 2018

### How does EX/IM money circulate?

Our evidence is persistent import surpluses accompanied by increasing foreign ownership of domestic debt. Can we justify speculation that unbalanced imports move capital from the ownership of (probably) eager buyers into the ownership of postponing buyers?

President Trump is concerned about foreign imports reducing the number of available domestic jobs. It is easy to see that foreign made products can have that effect by replacing domestic made products but what is the effect on the internal domestic flows of financial capital? We will find a plausible answer using logic and a mathematical relationship.

The Five Sector Rhythm Production Equation

The rhythm equation describes the productive evolution from initial labor to final product consumption in terms of capital and ownership. The five sectors are household $c,$ government $g,$ [both consumers] labor $n,$ private firm $k_p,$ and capital (money) $k_k.$The precedes-equals symbol $\preceq$ replaces the familiar equality symbol $=$ to remind us that production precedes consumption. The term $f_w$ relates labor hours to the unique currency of the domestic economy. $(1+k_k) n f_w \preceq c + g \pm k_p.$ The left side of the equation describes sectors that produce product for sale. The right side describes consumer sectors and the owning firm's profit. Product and time moves to the right with capital returned to owners at sale completion.

Figure 1. may help the reader understand the worker-to-consumer evolution.
 Figure 1. The equation's left side represents worker's time, conversion of time to capital, and the production of product. The right side represents consumption and a return of capital to the productive firm.
The 'Catastrophic Transfer Dilemma'

A quick glance at this equation might leave the reader thinking that all of the capital in the economy could end up in the ownership of the left side of the equation. Well, that won't happen if the owners and producers (who are mostly workers) are actually consumers (shown in Figure 1). If we assume that people receiving money also spend money, there will never be a 'catastrophic transfer dilemma'.

What about foreign trade, particularly unbalanced trade, where external economies acquire considerable ownership of domestic capital? As of February18, 2018, offshore investors have invested $6291.6B in United States Government debt, or about 31.5% of current GDP. China ($1176.7B) and Japan ($1059.5B) have accumulated combined debt valued at about 11.2% of current GDP ($19965B). Do we have a slow moving catastrophe here?

We can model foreign production with a generalized production equation. This is easily done by denoting net imports $k_\text{ni}$ and writing $(1+k_k) n f_w + k_\text{ni}\preceq c + g \pm k_p.$Now the equation shows foreign imports with a share of the domestic production marketplace. Foreign production will be purchased with domestic currency. While in the case of domestic production, we assumed that 'money earned will be money spent', that condition is glaringly absent in the case of unbalanced imports. Therefore, alarmingly, the equation gives us cause to predict that a catastrophic transfer dilemma is possible should importers continue to delay spending the monetary resource.

Any value received from sale of imports (which were initially produced using a foreign currency) is pure profit in terms of the domestic currency. The implication from this knowledge is that imports should be modeled exactly like the finished domestic product, which is what we have done. Both domestic production and imports are forms of 'capital' at this point of entry into the equation.

Imports Counter Stimulus Efforts

Imports are recognized as a transfer of capital between two currency systems. This type of transfer will leave a capital hole in the exporting economy and (after sale) create a newly filled deposit account in the importing economy. A natural (and probably safe) place to invest this new deposit is into the debt of the importing nation's national government (which seems to have happened in the United States).

To the extent that domestic workers buy imported goods, the pool of consumer money eagerly awaiting spending is reduced. To the extent of the reduction, the demand for government bonds is increased. Hence, government stimulus activity is directly countered by import purchases when not balanced by exports (Figure 2.).

 Figure 2. Net Federal Government Saving less Net Exports of Goods and Services. The remaining stimulation to the economy has varied widely over the last 20 years.

Conclusion

We have a coherent model that supports speculation of capital migration from eager spenders into a postponing ownership.  Perhaps we should be gratified that actual data confirms that possibility as an actual event, albeit as a slow moving evolution.

Domestic money flowing into unbalanced import accounts can be cycled through the lending process while awaiting permanent decisions. A loan to government is one of several possible money absorbing possibilities.

(c) Roger Sparks 2018

## Wednesday, April 25, 2018

### The Curious Rhythm of the Productive Economic Sector

$(1+k_k) n f_w \preceq c + g \pm k_p$
==================================
"It takes money to make money"  entrepreneur's adage
==============================================

When I think of money, I make an immediate connection with property as in 'property of all kinds'. My mind wants to stop there, leaving property connected to money.  Period.

Creating a mathematical envelope

Property has value, and money can buy property. Economist can all agree on that single connection.

Economist might not so easily agree that this single connection allows us to equate money with property in a barter fashion. I think we can say that one gizmo $g_z$ has a value of $x$ money units, denoted $xM_u.$ We can write that as $g_z=xM_u.$This equation gives us two ways of describing one gizmo, $g_z$ or $xM_u.$ The math does not care what a gizmo or money actually represents. It only says that a link has been established between two symbols.

This connection between gizmo and money opens the possibility that money can be created by making gizmos. The reader's reaction to that statement is probably an objection that only banks can 'create money'. But think of the possibilities if someone with-no-money can bring together an organization to produce a product. If selling the product brings more money than the cost of production, the organization will 'make money'. Not 'make money' in the sense that banks make money, but 'make money' in the sense that money is transferred from others into the control of the organization.

One barrier to bringing this concept to fruition is the acquisition of initial capital. The old adage "It takes money to make money" holds true here. Money must be paid to workers and part suppliers during production. Preexisting money must be acquired before producing complicated items that take considerable time in production.

Is this concept micro-economic or macro-economic?

The productive firm must bring together more than preexisting money. Several macro-economic sectors must work together to accomplish a task of product construction and sale. We have a situation where a single entity (the micro-economic productive firm) is fractionally organizing the economy in a macro-economic way.

And let's face it--any member of any sector has the ability to disrupt or delay the workings of this prospective productive machine.

Let's make a gizmo (with a little math)

Let's think about producing a gizmo. Just to make the task easier, let's think about making a complicated gizmo that requires a lot of workers to make, and requires a lot of time to complete.

It is easy to see that we need workers to build a gizmo. These workers need to be paid on a regular basis, which explains the predicted need for preexisting money. Parts and a host of other things would also need payment with money. Money for this purpose, often called risk capital, can be borrowed (from a number of sources). The borrower will expect to pay a rent (often an interest charge) for any money borrowed. This rental cost is an ordinary expense for the productive organization.

Mathematically speaking, we can describe the cost of construction of our gizmo $g_z$ in a very general way as $g_z \mapsto k_b + n$ where $k_b$ is borrowed money and $n$ is hours of labor**. This description is not an equality. To build an equality that describes actual cost we need to adjust hours of labor into terms of money, thus fulfilling the worker's adage "Time is Money". We also need to adjust the borrowed money term using the rental rate to build-in the effective expense of capital. We define the labor adjustment rate as $f_w$ and the rental adjustment rate as $k_k$.

In a very general way, we can write our gizmo production cost as

(1)      $g_z=(1+k_k) n f_w.$    ***

We could make the equation more exact by including exact units and a limiting time period but that would go past the scope of this article.

Close the envelope with sales

The goal of our productive firm is to 'make money'. Construction of the gizmo so-far has done nothing but cost money. This method of making money is obviously risky.

If we recognize this risk as a certainty, we can safely assume that expenses are very unlikely to equal income from sales. Rather than expecting sales to equal cost in general, the expectation should be for error between plans and reality. The challenge for the productive firm is to make this error favorable to them so that a profit $k_p$ can be recorded and the firm can in reality make money.

We close the envelope by assuming that the general public $c$ and government $g$ will buy this product. [We make no assumption about where money for purchase will come from, only assuming that money is available.] Assuming that customers pay the price in money, we can almost complete our mathematical envelope. I say "almost" because it is not clear mathematically that production must precede sales if we simply equate income with expenses and profit. To make that time-sequential process mathematically clear, we will replace the equality symbol with the "proceeds or equals" symbol $\preceq .$ **** The reader should understand that production proceeds sales and the final profit calculation. This is the sensitive rhythm previously mentioned. With all this in mind, we write

(2)       $(1+k_k) n f_w \preceq c + g \pm k_p.$

Equation 2 represents the flow of money for the construction and sale of any property. The actual physical property flows from left to right as does money used to finance construction. While the order of events is shown, the time required to accomplish all this activity is not represented here.

In real world accounting, Equation 2 is computed by taking data from a time period, usually one year. This practical practice hides time sequential dependency and plays havoc with theoretical models. We will not discuss the consequences of this theoretical gap here but will keep the possibilities in-mind for future discussion.

Rehashing sectors

Five commonly defined economic sectors have been included but their location in the equation may be obscure. Household $c$ and government $g$ are easy to locate as is a very stylish version of labor $n.$ The entire equation is about the productive entity making a gizmo but only the profit term $k_p$ is mathematically present.

The pure capital owning sector, denoted  $K,$ is represented by the interest term $k_k$ and is nearly invisible. Hidden is the risk capital that this sector provided to pay labor. Hidden is the decision to take a risk and build our gizmo. Hidden is the discontinuity that a negative decision by a capital provider introduces into beginning the process. Whether privately owned or government owned, upfront risk capital proceeds all production.

We can sum the sector rehash with a math function. I think we can say that a single productive firm $P$ can be described with a macro-economic function $P = F(c,g,K=k_k,n,P=k_p)$scaled to single firm size.

Should we call this a "five sector rhythm model of production"?

Confirm expansion of the envelope into macro

Equation 1 was clearly developed by using micro-economic thinking using macro-economic interactions. Equation 2 expands the model to include the flow of money during both production and consumption. There is no reason that the equation can't be expanded to the pure macro-economic level by adding product production of all kinds. The equation should apply to both privately and publicly owned productive firms. The only difference between the two ownership models is the emphasis on who owns what and who makes decisions.

A Thought for the Future

The "proceeds or equals" symbol is potentially very useful to the study of economics. It enables an ability to mathematically show time sequences or mutually interacting flows, and even circular flows if we begin and end the equation with the "proceeds or equals" symbol. For example, to show symbolically a circular money flow in Equation 2, we could write

(3)      $\preceq (1+k_k) n f_w \preceq c + g \pm k_p \preceq.$

In text, we could indicate whether the intent was to focus on macroeconomic money flows or micro-economic flows.

This example mathematically expresses a money flow from production to consumer and back to production. It does not carry any indication of the velocity of the flow. It worth mentioning again that this circular flow is very sensitive to the decisions of sector members, any one of whom can disrupt the flow to the extent of his abilities.

[This flow of money back to production is VERY important. It it this return flow that allows the production sector to repay the initial loan that enabled the entire productive effort. If we think about it, we can see that a speedup in the velocity of production and money flow allows multiple items to be produced and sold for the same amount of startup money. This can be considered as an increase in the efficient use of capital, thereby reducing overall cost of production. This is one factor favoring mass production.]

Conclusion

We found that we can create a symbolic representation of the micro-economic or macro-economic productive event with five united sectors. The productive event takes place over time with a sequential rhythm.

It is tempting to overlay the five sector rhythm model with the hyperinflation occurring in Venezuela. While little confirmed data is available from Venezuela, it appears that government has preempted production decisions, causing disruption in the profit learning sequence. Government may be acquiring money for purchases not by working at productive effort (through taxes), but by borrowing money as if government was, in itself, a producing firm. This practice distorts the balance between customer need, willingness to work, and relative perceived value of natural resources. This harmful practice may be more obvious to foreign economies than to the borrowing economy, triggering sharp decreases in currency value.

The commonly used equality symbol $=$ does not give any hint of the time-sequence-dependent relationships typically found in the study of economics. Economic discussions may be enhanced with increased use of the "precede equals" symbol.

Mainstream economist often mistakenly claim that profit is the reward of capital. The reward of capital is interest. Profit is the reward of the productive firm for acting to organize production.

==================================
Footnotes:

* This article, emphasizing the importance of circular money flow, is a follow-up to a previous article on the same subject and includes several enhancements. Neither article would have been written but for a series of articles written by Brian Romanchuk. His "Curious" series of four articles explored the logic behind DSGE models in an unflattering way.

** The reader may not be familiar with the mapsto $\mapsto$ symbol. The intent is to indicate that there is a relationship between the left and right side of the equation but no reason to expect equality.

***  $g_z=nf_w + k_knf_w =(1+k_k) n f_w.$

**** When we write $x \preceq y,$ we intend that $x$ precedes or equals $y.$ TeX and LaTeX symbols can be found here.

(c) Roger Sparks 2018

## Saturday, March 24, 2018

### The Curious Union of Chess, Money, and Economic Production

$c(t)+g(t)=r(t)k_b(t)+f_w(t)n(t)+k_p(t)$
$c(t) + g(t) = f_w(t)n(t)(1+r(t)) + k_p(t)$
$c(t) + g(t) = k_b(t)(1+r(t)) + k_p(t)$
==============================================
In the game of Chess, players own the moves they make. Each move advances the game in a continuum from start to finish.

A productive firm works the same way. When a fractional part of a complex product is made or purchased, the firm owns another fractional part of a continuum that evolves into a priced product.
In a curious way, I'm frustrated by Brian Romanchuk's article
"The Curious Profit Accounting of DSGE Models." I can't convince myself that his beginning equation 16.2.3 is correct.[1] [2] It certainly doesn't fit with the real-world economic framework that I observe!

Unable to make sense of the equation but agreeing that an equation linking three sectors of the productive economy is a worthy goal, I would like to remove the wrinkles. A task harder to do than I expected.

The Problem

While my initial criticism of the equation was the number of sectors represented, I eventually realized that the basic flaw stemmed from a misuse of the capital tool. Financial capital was conceptually used as means of production in the same manner as labor so that it became one of the final products. That made no sense to me. In the real world, financial capital is directly exchanged for fractional contributions thereby transferring ownership in both directions.

We can use the example of fractional labor as an illustration to make the point. Using monetary exchange, one current hour of labor is traded for an hour of labor-that-has-been-previously-completed. In other words, when a person works one hour, that effort is effectively traded monetarily for one past hour that another person has sweated through.

The Solution

We can symbolically show past laboring effort expended, then represented by financial capital, and then returned to labor by writing  $n \mapsto k \mapsto n,$ where $\mapsto$ is the maps-to symbol, $k$ is the capital received from previously expended effort and $n$ is hours expended either past or currently.

This symbolic description using money [5] does not relate hours directly to a rate of payment. It has the limited task of indicating that a block of labor has been traded for a block of money has been traded for a block of labor. The concept of trading blocks for blocks will be woven into this article.

Only by accident does perfect mapping occur in real world exchanges that occur over a time period. Instead, there is always a difference in values that we will describe symbolically by writing  $n \mapsto k \mapsto (n+p),$ where $p$ represents a value difference perceived by the owner of the second $n.$ In words, we say that the second provider of labor must perceive a benefit (or Profit) that encourages a decision to proceed. The benefit may be visible in the form of money or invisible in the form of product preference.

Continue  Defining Sectors

Returning to the subject of sectors, my initial criticism of Brian's equation 16.2.3 was that four sectors were described, not three as he suggested. Now that I am in version 6 (or more!) of developing a 'better equation', I believe that FIVE sectors are required to fully describe the productive economic continuum.

How do I define 'sectors'? If an economic contributor can make a decision, there is a need to represent that ability by assignment to an economic sector. The ability to make a decision implies ownership of some part of the productive amalgam with entitlement to financial reward. The five sectors that I see are consumption, government, productive firm, labor, and financial capital.

The productive firm sector will be assigned a reward coming from profit (if any).

The need for a financial capital sector is not immediately obvious because each of the other sectors have within them members who own financial capital,  The need for a separate sector stems from the ownership impairment decision that must be made when property is rented away.

Our capital sector will have a undefined stock of preexisting capital. This will be a necessary assumption when we later assume that productive firms borrow and repay all financial capital used to pay expenses during a time period. The capital sector will be assigned a reward in the form of interest payment.

Describe Model Conditions in a Nutshell

The task of a productive firm is to reorder the capabilities of our five sectors into a product exchange evolution. The assembly process will be measured and modeled as a capital expense using three sectors: 1) a stylized all-inclusive labor sector, 2) a sector describing the cost of rented capital, and 3) an unpredictable remainder (Profit?) assumed to be owned by the productive firm sector. The selling process (of the product for consumption by the household and government sectors) provides income. The entire process is assumed to start and complete in one year.

Capital (owned by the capital sector) is existent and adequate. Financial capital is traded fractionally for fractional product parts as the product is assembled and finally sold.

Now Write a Productive Continuum Equality

We will describe the productive process by completing an annual income statement in terms of our five economic sectors. The result is surprisingly satisfying.

Our income statement will be written directly from the description given.[4]  Label the sector terms as labor $n,$  borrowed capital $k_b,$ profit $k_p,$ household $c,$ and government $g.$ With income on the left side, we write the general concept mapped to the real-world as $c+g \mapsto k_b+n+k_p.$ where profit is the incentive  term.

Before writing an equality, we need to adjust the data from each sector into a place on the monetary scale, noticing that only the labor sector is not already reported in monetary terms. We will adjust labor by using a translation factor $f_w.$  The cost of borrowed capital will be calculated using cost factor $r.$

To do all of this, we will use a function format[3] with a time notation to indicate that the equality is related to a unique time period. We will write our equality as

(1)       $c(t)+g(t)=r(t)k_b(t)+f_w(t)n(t)+k_p(t).$

Equation 1 bridges the continuum of the productive process using five sectors.

Readers may be interested in comparing equation 1 to Brian's equation 16.2.3. In 16.2.3,  terms $k_b(t)$ and $f_w(t)n(t)$ seem to have been equated which enables us to simplify the equation. This is allowable if capital is borrowed at the same time and amount that labor cost are paid (albeit an inefficient process). With stylized labor cost clearly paid with borrowed capital, we have  $k_b(t) = f_w(t)n(t).$ Substitute into equation 1 using the labor term to get $c(t) + g(t) = r(t) f_w(t)n(t) + f_w(t)n(t) + k_p(t).$ Simplify to read

(2)          $c(t) + g(t) = f_w(t)n(t)(1+r(t)) + k_p(t).$

We can also substitute using the borrowed capital term to get

(3)         $c(t) + g(t) = k_b(t)(1+r(t)) + k_p(t).$

The difference between expressions (2) and (3) is the emphasis on financial capital or labor. The two expressions should evaluate to the same monetary number.

Equations 1, 2 and 3 are all final versions of an equality that I think describes the productive continuum adjusted to the real-world using five sectors. Perhaps my readers will have a better definition of exactly what the equation describes.

Unfortunately, Brian's 16.2.3 looks like a distant cousin of the equations developed here. I still don't understand 16.2.3.

Making the Unknown Known

In the assumptions (in "model conditions"), we clearly stated that profit $k_b(t)$ was unknown, yet, we also clearly assumed that the entire equation completed in one time period. If completed, we can learn the value of all terms by examining the accumulated data.

Equation 1 (and equivalent 2 and 3) describes a relationship between economic sectors. It would be correct to attach a historical number to each of the sectors. It would also be correct to predict future numbers for each sector based on changes envisioned.

DSGE models supposedly try to find points of optimization for the sector of interest. The equations developed here would suggest that optimum for one sector would not be optimum for a second sector.

Using the Equation

It is important to remember that the profit term $k_p(t)$ is a balancing term that maps theory to the real-world. Hence, we should NEVER expect to find numerical values by beginning with a known profit result. Yes, the profit term is real in the real-world, but it represents motivation (or disincentive) for decision makers at the theoretical level.

This model of money and it's use in productive effort seems (to me) very robust. As a robust description, it can become a common reference for departure into other, hopefully improved, models. Three model excursions follow to illustrate this possibility:

1)  This productive continuum equation was built based on micro economic principals. It can be smoothly expanded to the macro economic scale by adding productive firms. When ALL of the productive firms are included, we can begin consideration of the catastrophic transfer problem [If productive firms are always profitable, eventually all of the money available in an economy will be in the ownership of firm management.]. This undesirable conclusion could materialize using this model if financial capital ownership was not widely distributed in the economy. Would government ownership of capital prevent the potential problem?

2)  We can easily model a government that uses two revenue sources, bonds $g_b(t)$ and taxes $g_t(t)$. We could write the equation as $c(t) + g_b(t)b_k(t)+g_t(t) = f_w(t)n(t)(1+r(t)) + k_p(t)$ where the term $b_k(t)$ converts the bonds to financial capital. This model would need an explanation for how that conversion mechanism worked in the real economy.

3) Still using the model of example 2, which government would be more interested in imposing tariffs and why?

Hmmm. How would we fit foreign sourced production into an equality like we have here? I don't have that question resolved.

Conclusion

A DSGE equation that seems to not fit smoothly with other frameworks caused enough irritation to initiate an effort to find a better fitting equation. The better fitting equality found requires a base framework of assumptions that clearly included a capital owning sector that had decision making authority.

The simplicity of the equation found makes it seem almost trivial. Yet, we needed to assume a robust continuum of sequential money transfers before we could logically connect fractional construction to finished priced product. We also needed to divide the economy into sectors, each with decision making capability and with the ability to contribute to the productive or consumptive processes. The simplicity of the equation hides the rigidity of the required assumptions.

 The management role of decision makers has barely been considered here. The role of a lender supplying initial capital is particularly important. This productive continuum model is discontinuous at the starting point. If a lender fails to allow initial production, nothing happens! In a similar fashion, labor, whether organized or individually represented, has a decision making role. Labor is supplied hour by hour. A discontinuity is reached if labor decides to not perform. In the real economy, consumers can borrow money to buy goods. It is easy to see in this model that production would be stimulated by customer borrowing. Government borrowing may be sustained sequentially over time, potentially forming a mechanism for hyperinflation. Thanks to Brian Romanchuk for his efforts to present this series of articles. [Brian's final article in the series can be found here.] ============================================== [Note 1] One of the nice things about beginning a study of economics when you are older is that you have a lot of experience from which to draw. One of the frustrations is that you may have little or no economic schooling to guide you. This places you in the position of learning everything about economics from the position of being a well educated beginner. I resist accepting economic theories until each element can fit seamlessly with the mating theories, like in assembling a jigsaw puzzle. [Note 2] This article contains an expanded explanation of the equations first presented (by me) in a comment in Brian Romanchuk's article at http://www.bondeconomics.com/2018/03/the-curious-notation-of-dsge-models.html#comment-form. [Note 3] Function notation is a method of mapping inputs into a repeatable pattern. The time term $t$ as in $f(t)$ indicates that the data is accumulated over a time interval. [Note 4] Term $n$ represents hours of labor. We will use hours of labor as a proxy for all cost of production whether purchased directly as labor or hidden in a bid price for a part or service. The actual expense of a widget is not of concern here. We are only interested in learning the interactions between borrowed money and other sectors. If we later are interested in other interactions, we may need to refine our definitions. Hours of stylized labor must be converted to a financial capital equivalent using term $f_w$. [Note 5] The terms 'money', 'financial capital', and (occasionally) simply 'capital' are used somewhat interchangeably in this article. 'Capital' is never used as a reference to fixed capital such as buildings or bonds. (c) Roger Sparks 2018

## Sunday, March 4, 2018

### Tariffs, Sales Tax, and a Stronger Dollar

President Trump has proposed placing a 25% tariff on foreign steel and a 10% tariff on foreign aluminum. How in the world are we supposed to analyze that action?!

Well, maybe it's not so hard. This would be the United States government imposing a tax on all steel and aluminum that moved across borders. The tax would be paid in American dollars, not in the currency of the country of origin. It would be paid by the customer buying steel or aluminum should the customer chose a foreign made source.

Hence, we see here that an American steel consumer would be asked to make a choice of supplier, knowing that choosing foreign would result in a higher price due to the tax imposed. Considering only the tax implications, what is the relationship between the domestic and foreign prices?

Tariffs are a sales tax

A customer may have a choice between two governmental taxation schemes. If a customer has the choice of paying a sales tax or not, it makes no difference to the customer which government imposes the tax. The only differentiation is the relative price for the product. With this in mind, a tariff can be considered the same as a sales tax, the only difference being which government imposed the tax. This realization allows us to consider the situation of a customer living very close to a border between states, one state charging a sales tax and one not charging a sales tax. (The states of Oregon and Washington come to mind.)

A steel customer in Oregon (no sales tax) buying steel made in Washington would pay a 8% (about) sales tax. How would this customer make a purchase decision?

The sales tax or tariff decision

We will ignore the cost of transportation and other distance and time considerations to focus only on the tax consequences.

Our customer would find the point of price indifference where the price of product from each source is the same. In mathematical terms, the point of indifference occurs when

Oregon Price = Washington Price + Washington Price X Tax Rate

= WP + (WP X TR)
= WP(1+TR)

Transposing, we see that the point of indifference occurs when

Washington Price = OP/(1+TR).

Still ignoring transportation cost and using the 8% sales tax rate,  we can calculate that the Washington Price must be 0.926 or about 7.4% less than Oregon price before the price advantage shifts to Washington's favor.

With this background, we can consider President Trump's proposal from the standpoint of a steel purchaser. If a American steel customer must choose between foreign steel which carries a 25% tax and tax free domestic made steel, the foreign steel must be priced at less than 1/ (1 + 0.25) = 0.80 of domestic price.

Of course, in the real economy, transportation cost and other factors would be considered additionally.

A new tariff impacts three groups

Everyone dislikes taxes so it is certainly understandable that proposal for a new tariff would bring protest from the impacted parties. We can broadly group impacted parties into three groups: tax payers, disfavored suppliers and favored suppliers.

Broadly speaking, the domestic taxpayer will be the customer who must pony-up the tax payment. With a new tariff, government is raising the cost of product to the consuming public. This invokes the cost related supply-demand factors that we commonly study in economics.

Disfavored suppliers can be expected to lose sales to favored suppliers. This will again set into motion the supply-demand factors that we commonly study in economics, with opposite-trending local effects on the two supply groups.

It is interesting to consider the longer term macro-economic interactions of these three groups. A tariff will quickly cause a reduction of foreign trade accompanied by a transferred increase in domestic demand for the tariff-taxed product. Moreover, because domestic taxes are increasing for the tariff imposing nation, the strength of the domestic currency will INCREASE. This makes it more difficult for the foreign nation to obtain currency so we would expect an immediate decline in purchases of all products. It follows that a tariff imposing nation should expect to see fewer sales to other national economies as well as slower domestic sales.

The economy shifting effects of tariffs

In the longer term, the macro-economies of the victimized economies can expect to see permanent economy shifting effects. In the case of steel, the local price of steel should fall (due to less demand) but that makes the cost of producing other products less expensive which would (in the longer term) improve sales (including foreign sales) of products made using steel.

The general effect of tax streams on governments

We need to further consider the effect of a tariff on the finances of the imposing country. The most important part of this consideration is that the tax will be paid in the currency of the imposing government.

The tariff imposing government will have a new income stream. This stream will come from tariff paying customers. Additionally, if the taxed product is a basic building material like steel, then we can certainly expect to see the cost of the tax flow into all new construction. To the extent that cost increases result in higher tax flows (such as results for Washington state sales tax) general governmental revenues increase.

In the case of the American federal government, the imposition of a tariff should rapidly increase income taxes coming from the steel industry as wages and profits rise in response to increased/transferred domestic demand.

The foreign taxation dilemma

The last tax effect that we will consider in this post will be the dilemma faced by governments as they tax to pay for government needs. How do you tax labor and production facilities that reside outside national boundaries?

Consider a government dependent upon the income tax to meet a large portion of government cost. Apply that dependency to build a contrast between domestic production and foreign production. It is safe to assume that domestic producers will be subject to the income tax while foreign producers will avoid this tax. How does this difference distort trade?

The effects are not immediately obvious. What is clear is that foreign workers would not contribute to the tax needs of domestic government. In that sense, foreign production arrives at the border tax free. On the other hand, these same foreign workers have better incomes earned from the economy supporting the tax deprived government. Presumable these foreign workers pay taxes to their own government, but the money paid comes from the tax deprived economy. [Post Note: Yet, foreign workers are paid in a second currency, not the currency of final sale. In the absence of balanced trade, some entity must absorb a trade of paper for product.]

The synergy described sets up conditions encouraging every government to support foreign sales, with a goal of increased government revenue due to more income tax paid. Of course imports have the opposite effect.

As if it were a surprise, we can conclude that taxation can have economy shifting effects.

Conclusion

It seems to me that a better sales effort needs to be made to sell a new tariff on steel and aluminum. This new tax would be easier to accept if the need to bring foreign production into a tax sharing mode is made clear (to the public). Domestic governments would like all producers to fairly help pay for government programs, (thus sharing the tax burden laid upon domestic producers). Of course, domestic customers prefer buying foreign if they can get a less expensive product, ignoring (or even relishing) the probability that avoidance of domestic taxes may be the reason for lower price.

To the extent that tariffs better-balance the tax burdens of government, tariffs seem reasonable.

An afterthought

Disfavored suppliers, victimized by a new tariff, will be understandably upset by what is perceived as being discrimination against them. They will take it personally.

Governments housing these same disfavored suppliers are likely to attempt to find new markets, keeping workers and factories in a production mode. New markets, if peaceful, can be good. However, these same (in the case of steel) production facilities can be used in markets producing ships, tanks and other weapons, which would not be good. Thus we see a danger in forcing rapid changes in economies by using blunt trade weapons such as tariffs.