Wednesday, March 27, 2013

Money Supply and the Exchange Rate

Ever wonder what happens to the foreign exchange rate when the Central Bank makes a pronouncement to either decrease money supply circulating around or slow the growth of that money supply over a number of years?

There is no simple, one-line answer to this. Firstly, when evaluating the effect of this policy on the economy, we need to decide whether we are taking on a short- or long-term perspective on its effects. Short-term effects of a policy do differ substantially from the long-term effects of such. Secondly, we need a framework, model, or theory, or a ‘lens’ if you will, with which to view the path by which the series of economic events take place after a policy trigger and that will enable us to predict outcomes.

Last week, I gave an exercise to my class in international trade and finance to analyze the economic effects of the Chinese Central Bank’s recent policy pronouncement that it will work to slow down the growth of its M2 money supply from 13.8% to 13% in 2013 (‘China reforms needed to lower M2/GDP ratio - c.bank chief’, Reuters, 8 March 2013).

China’s M2 money supply

Money supply is defined as the total monetary assets in an economy, generally consisting of the total currency in circulation including demand deposits (or checking account). There are different ways to measure the money supply, depending on how narrowly or how broadly it is defined. Thus, money supply is typically classified along a spectrum or continuum between narrow and broad monetary aggregates. Narrow measures include only the most liquid assets, the ones most easily used to spend (currency units, checking accounts). Broader measures add less liquid types of assets (savings accounts, time deposits, and other certificates of deposit).

For example, the US defines money supply into the following categories: M1, M2 and M3. M1 consists of currency (and traveler’s checks), demand deposits, and NOW and similar interest-earning checking accounts. M2 comprises M1 plus savings deposits and money market deposit accounts, small time deposits1, retail money market mutual fund balances. M3 is M2 plus large time deposits, institutional money market mutual fund balances, repurchase agreements, Eurodollars (The Federal Reserve System, 2005).  

In the Philippines, money is defined or classified into: M1, M2, M3 and M4. M1 or ‘narrow money’ consists of currency in circulation (or currency outside depository corporations) and peso demand deposits while M2 or ‘broad money’ comprises M1 plus peso savings and time deposits. M3 or ‘broad money liabilities’ is M2 plus peso deposit substitutes, such as promissory notes and commercial papers (i.e., securities other than shares included in broad money), while M4 consists of M3 plus transferable and other deposits in foreign currency.

In China, the relevant money supply for monetary policy is M2. Chinese M2 money supply consists of money and quasi-money currency, demand-, time-, savings- and foreign currency-deposits held by sectors other than the Chinese government. It stood at 85.2T yuan in 2011, which expanded by 17.3% from the previous year and by an average of 18.5% per year over the past 10 years (see Figure 1). By end of 2012, it exceeded 97.4 trillion yuan ($15.5 trillion) making it the world’s largest money pool, 1.5 times that of the United States--an economy 1.9 times larger (in terms of GDP) than China's in the same year (IMF 2012). 

Figure 1. China’s M2 stock

Further, Chinese M2 stock represented an astounding 180% of GDP for the year (see Figure 2). By 2012, Chinese M2 level reached 188% of GDP, considered the highest among major economies in the world.

Figure 2. China’s M2 as % of GDP

It is perhaps for this reason among others, that the Chinese Central Bank has set a 13% annual growth target for M2 money supply in 2013—slower than the 13.8% actual growth in 2012, and way slower than the M2 growth seen in previous years which saw a 47% growth in 1993 and a growth of 28.4% only three years ago in 2009.

With this backdrop, I asked my students to take on a long-term perspective and determine the long-run effects of such policy on key economic variables in the Chinese economy. In particular, I asked them to determine the policy’s effects on the Chinese price level, inflation, the yuan currency deposit interest rate, the Chinese yuan (CNY) exchange rate with the US dollar (USD), and on total economic output. They were also tasked to compare and contrast these effects if the policy were a one-time decline in money supply, and to explain what the Chinese monetary authority wants to achieve with this policy over the long term.

Long-Run Exchange Rate Model Based on Purchasing Power Parity (PPP)

The model or theory of choice for our class to analyze the impact of the Chinese Central Bank’s policy was the Long Run Exchange Rate Model Based on PPP—among the popular models floated around in standard textbooks in international economics because it is both simple and intuitive as it looks at the path by which changes in the money supply have far-reaching effects not just on the general price level but also on other economic variables such as the interest rate and the exchange rates.  

This model, in a nutshell, says that purchasing power parity (PPP) will hold in a world where there are no market rigidities to prevent the exchange rate and other prices from adjusting immediately to levels consistent with full employment (Krugman, et al, 2012, International Economics). Specifically, it assumes two (2) conditions to hold in the assets market: 1) the expected relative PPP condition, and 2) the ‘Fisher effect’.

The expected relative PPP is given by this equation:
(exp Eα/β – Eα/β)/ Eα/β  = exp π (A) – exp π (B)
where,
exp Eα/β = the (future) expected exchange rate between currency of country A, (i.e..α) and currency of   country B (β)
Eα/β = the exchange rate between currency of country A (α) and currency of country B (β)
exp π (A) = expected inflation rate in country A
exp π (B) = expected inflation rate in country B
which implies that a currency depreciation (or appreciation) is expected to offset international inflation differences or inflation differences between two (2) countries at a rate of (πΔπ).

In this model, if people expect relative PPP to hold, the ‘Fisher effect’ shall also hold: the difference between the interest rates offered by any 2 type of currency deposits will equal the difference between the inflation rates expected over the relevant period in the 2 countries that own those currencies.

The ‘Fisher effect’ is given by this equation:
            R(α) – R(β) = exp π (A) – exp π (B)
where,
R(α) = deposit rate for currency α in country A
R(β) = deposit rate for currency β in country B
exp π (A) = expected inflation rate in country A
exp π (B) = expected inflation rate in country B
which implies that, all else equal, a rise (or fall) in a country’s expected inflation rate will eventually cause an equal rise (or fall) in the interest rate that deposits of its currency offer.

Economic Effects of a Slower M2 Growth

Using this long-run model, Chinese M2 growth slowing to 13% (assuming this is a constant rate by which M2 will grow over time) will thus require an ongoing fall in the Chinese price level at the same rate, and hence lead to a decline in inflation in order to keep real incomes in China constant.

While the model assumes such changes in the price level and inflation will not affect full employment output level and the relative prices of goods and services, it does assume to have an effect on interest rate via the ‘Fisher effect’.

By the ‘Fisher effect’, a fall in the inflation rate will eventually cause a fall in the Chinese interest rate or the CNY deposit interest rate. Thus, the continuing slowing of Chinese M2 growth will eventually affect primary interest rates in China in the long-run and cause it to decline. 

By the expected relative PPP condition assumed also to hold in the long run, the fall in the price level brought about the fall in Chinese M2 growth will also create a simultaneous proportional downward fall in the exchange rate between the Chinese yuan (CNY) and say, the US dollar (USD)—the currency of its most important and largest trading partner, the US.

Thus, all else equal, a decline in Chinese M2 growth will require the ongoing fall in the price level and hence a fall in expected inflation rate, which eventually will result in the decline of the CNY deposit’s interest rate, and by virtue of the expected relative PPP assumed to hold in the long run, will likewise cause a fall (or an appreciation) in the exchange rate between the CNY and a major currency such as the USD.

To conclude, a decline in M2 growth rate will lead to a fall in the price level and inflation, a decline in the CNY currency deposit or interest rate, and a CNY that will be stronger in the future.

(By how much or to what extent will those economic variables rise or fall in value with the decline in M2 growth can be estimated econometrically but is something beyond the scope of the course for my class.)

Meanwhile, we expect such policy to have no effect on long run full-employment output. Long run full-employment output is influenced by non-monetary factors such as changes in the level, quality, and productivity of a country’s factors of production via technological innovation, and similar causes. Further, in the long-run, as posited by Irving Fisher in his work The Theory of Interest (1930), purely monetary developments should also have no effect on an economy’s relative prices, and hence provide a cause for reallocation of consumption or production in the economy.

Now that we know what could happen to the economy when the money supply growth slows down, it begs asking why would the Chinese government want to do this, and what does it want to achieve with this policy?

The Goals of Monetary Policy

The purpose of the exercise I gave in class was to demonstrate monetary policy in action and to gain understanding what monetary policy wants to achieve in the economy at large and in the assets market in particular.

The goals of monetary policy are generally the same across market-oriented economies, with just slight variations on the means and extent. In the US, the goal of monetary policy is “to promote effectively the goals of maximum employment, stable prices, and moderate long-term interest rates.” (Board of Governors of the Federal Reserve System, 2005).   

In the Philippines, the primary objective of monetary policy is “to promote price stability conducive to a balanced and sustainable growth of the economy” in accordance with Republic Act 7653 (Bangko Sentral ng Pilipinas, 2012), with inflation targeting as the explicit framework by which to achieve this objective and price stabilization an ultimate goal.

While monetary policy such as changing money supply levels or its growth will undoubtedly have effects on the price level and inflation, as our model has illustrated, it will likewise have concomitant effects on interest rates and currency exchange rates. In reality, it does in fact have such effects.

Why does China want to slow its money supply growth?

After 5 years of double digit growth post-1997 Asian financial crisis (2003-2007), China’s gross national income (GNI) began to slow by 2008 to 9.6%--still fast by world standards but relatively slower nonetheless. In recent years too, inflation has begun to creep in, from a mere 1.4% in 2006 to 5.4% in 2011—relatively low again compared to the world average but considering housing costs such as rent (which have been skyrocketing in recent years) have been excluded from the Chinese CPI, can lead us to surmise that this inflation trend is actually quite significant (see Figure 3).   

Figure 3. China’s GNI, GDP growth and Inflation

Theory says a policy to slow money supply will eventually lead to slow inflation, thus arresting the unnecessary price increase in the future thereby preserving the purchasing power of the Chinese consumers amidst a relatively sluggish economy.

But our prediction of economic outcomes based on theory does not stop there. The expected decline in inflation will all things equal, eventually cause CNY deposit interest rates to fall (or interest rates in general) and the expected CNY to appreciate relative to the dollar in the future.

In other words, slowing the growth of M2 in China will lead us to expect not only inflation to fall but also the price of credit (i.e. interest rates)—thereby providing a stimulating effect on domestic investments, plus a stronger CNY in the future--and along with it far reaching implications for the international movement of goods, services, capital, funds between China and the rest of the world. Whether the CNY—perhaps the most controlled currency in the world—will actually appreciate in the future--is a different story though.

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References

Bangko Sentral ng Pilipinas (BSP), ‘Glossary of Terms’. Available at: http://www.bsp.gov.ph/monetary/glossary.asp [Accessed 10 March 2013].

Bangko Sentral ng Pilipinas (BSP) Department of Economic Research, September 2012. ‘Primer on Inflation Targetting’, Available at: http://www.bsp.gov.ph/downloads/Publications/FAQs/targeting.pdf [Accessed 10 March 2013].


Board of Governors of the Federal Reserve System, 2005. The Federal Reserve System: purposes and functions. Washington, DC (USA): US Board of Governors of the Federal Reserve System.


Fisher, Irving, 1930. The Theory of Interest, New York: Macmillan.


International Monetary Fund, 2012. World Economic Outlook Database, October 2012, Available at: http://www.imf.org/external/pubs/ft/weo/2012/02/weodata/index.aspx [Accessed 13 March 2013].


Krugman, et al, 2012. International Economics: theory and policy, 9th edition, Boston, MA (USA): Addison-Wesley.


Reuters, [Online], ‘China reforms needed to lower M2/GDP ratio - c.bank chief’ Reuters [Online]. March 8, 2013, Available at: http://www.reuters.com/article/2013/03/08/china-economy-m-idUSL4N0C00BI20130308 [Accessed 9 March 2013].


The World Bank. World Bank Open Data--China Metadata. Available at:  http://data.worldbank.org/ [Accessed 10 March 2013].

Tuesday, February 19, 2013

The Effect of an Equal-Proportions Increase in Prices and the Benefits of Engaging in Trade


Recently I gave a mid-term examination to my Econ 190.1 class consisting of 40 items for multiple choice and 30 items for problem solving.

There were 2 items in the multiple choice part of the exam that generated so much confusion. Students were trying to argue with me what the correct answer should be for those 2 items.

I want to blog about it here, to help my students link the lecture with the exam items, grasp the concepts presented in class better, and understand why the answer to the questions are what they are.

So there were 2 contentious exam items, one about the effect of an equal-proportions increase in prices, and the other item about the benefits of engaging in trade. Clarifications and my explanations are presented herein.

Here's the first item--

ITEM 1--- 
‘9) In the specific factors model, a 5% increase in the price of food accompanied by a 5% increase in the price of cloth will cause wages to ________, the production of cloth to ________, and the production of food to ________.
A) remain constant; increase; increase
B) increase by less then 5%; decrease; increase
C) increase by more then 5%; increase; remain unchanged
D) increase by 5%; remain unchanged; remain unchanged
E) remain constant; decrease; decrease’

The correct answer to this question is ‘D’. 

Explanation--

In this exam question, we are asked to determine (in an economy where there only 2 goods—food and cloth and using the specific factors framework) the impact of a 5% increase in the price of food and a corresponding 5% increase in the price of cloth on the following: 1) wages; 2) production of cloth; 3) production of food. 

Recall that in the specific factors model (of P Samuelson and R Jones) discussed in Chapter 4 (Krugman et al, 2012), one of the conditions for profit maximization is that employers will demand labor up to a point where, 

the value produced by an additional person- or worker-hour = cost of employing that hour, 

which means, for each sector c (cloth) and f (food), the following hold true:

1) value produced by an additional person-hour (also called the value of the marginal product of labor) = MPL x P, 
where, MPL = the marginal product of labor in any sector 
P = the price of one unit of product in that sector
2) the value of output produced by an additional person-hour = hourly wage, w,
or, in equation form:  
MPLc x Pc = w
MPLf x Pf = w

Hence, any price increase of either cloth or food or both will increase the value produced by an additional person-hour (VMPL) in either cloth, food, or both respectively. 

To achieve profit-maximization (see condition 2 above), the VMPL must be = to w. Hence, an increase in price causing an increase in the VMPL, will have to be matched by an increase in wages, w.

In Krugman’s exposition, the effect of an equal-proportional increase of 10% in the price of both goods in a 2-good economy is best demonstrated in Figure 4-4, where VMPLc (cloth) and VMPLf (food) increase proportionately by 10%, and wages increase proportionately by 10% as well. Incidentally, such price changes will not induce any changes in labor allocation in the economy between the 2 sectors of cloth and food.


FIGURE 4-4. An Equal-Proportional Increase in the Prices of Cloth and Food

   

So, what happens to production levels for both cloth and food, arising from a case of ‘equal-proportional change in prices’ (i.e. 5% increase in the price of cloth, and 5% increase in the price of food)? 

To determine changes in production arising from changes in prices, we must look back again to the production function. 


FIGURE 4-5. Production in the Specific Factors Model



In the specific factors model, recall that another distinctive assumption of the model is the condition of ‘production efficiency’, which means, the economy produces at a point where the Production Possibility Frontier (PPF) must be tangent to a line whose slope is minus the ratio of the price of cloth to food (Pc/Pf)—see Figure 4-5.

Technically, the economy must produce cloth and food at a level where the slope of its production possibility frontier (or the transformational possibilities available in an economy toward increasing its aggregate output given its level of technology and resources), 

-MPLf/MPLc

Is equal to minus the ratio prices between cloth and food (representing society's relative valuation of cloth to food and vice versa),

-Pc/Pf

Or simply--

-MPLf/MPLc = -Pc/Pf

which essentially means that the economy is producing at its highest transformational possibility given its level of technology and resources and consistent with its society's relative valuation of all goods produced in the economy.

Going back to the exam question, in a case of an ‘equal-proportional change in prices’ where Pc increases by 5% and Pf increases also by 5%, its effect on the ratio of prices Pc/Pf will essentially be none. A 5% increase in Pc matched by a 5% increase in Pf will not change the value of this ratio. Hence, production levels in the 2-good economy embodied in the PPF will also not change.

To conclude, a 5% increase in the price of cloth, Pc matched by a 5% increase in the price of food, Pf will --- 
1) raise wages (nominal wages) by 5%
2) raise VMPLc by 5%
3) raise VMPLf by 5%
4) result in no changes in labor allocation between sectors
5) result in no changes in relative prices, Pc/Pf
6) result in no changes in production. 

Therefore, the correct answer to the question is D. 

Here's the next item,

ITEM 2:
‘10) A country that does not engage in trade can benefit from trade only if
A) pre-trade and free-trade relative prices are not identical.
B) it employs a unique technology.
C) it has an absolute advantage in at least one good.
D) its wage rate is below the world average.
E) pre-trade and free-trade relative prices are identical.’

The correct answer to this question is ‘A’ and not ‘D’. In fact, I was surprised when the standard test material referred to D as the correct answer. Smart also that my students insisted the answer was A and not D.

In chapter 4 of Krugman et al (2012), Krugman et al discussed international trade in light of the specific factors model and in so doing, made this proposition:

‘For trade to take place, a country must face a world relative price that is different from the relative price that would prevail in the absence of trade.’

The reality is, countries face domestic prices of goods and services they produce that are different from (or not identical to) prices of goods and services in the world. Countries have different technologies (Ricardian model) and resource endowments (Hecksher-Ohlin), giving rise to relative supply curves for the world different from domestic relative supply curves across any paired set of goods. 

Economies of the world can take advantage of the differences in relative prices and this is what really gives impetus to and rationale for trading with other countries. Hence, the correct answer is A.

Because my students were smart enough to call out these questions, these items were given as bonus points in the exam! :)

Tuesday, November 27, 2012

Trading at Optimal and Equilibrium Level


I teach undergrad economics at the country’s premier university. This semester, I’m teaching International Trade, Finance and Development Policy. 

The semester has just started and based on the course syllabus, part of the requirement is for students to learn (and for me to teach) about international trade models and theories as tools to analyze the causes and effects of trade between and among countries.

In a class I had last week, I got a question from one of my students, J, about the Ricardian One Factor Trade Model (Chapter 3 of International Trade by Krugman, et al) that puzzled me too. 

So I answered him the best I can in class but promised I would give a formal reply in our yahoo group and in my blog. 

Here’s my reply. 

During the lecture I discussed the Ricardian One Factor Model of Labor Productivity and Comparative Advantage, in particular, the part on Trade in the One Factor Model. 

In reference to Fig 3-3 (of Krugmans' book and shown below) showing the world relative supply and demand curves for cheese and wine, his question was, why would Home and Foreign not trade at point 2.

Let’s look at or review the assumptions of the Trade in One Factor model again:

  • 2 countries: Home and Foreign
  • One factor of production in each country: Labor 
  • Each country can produce 2 goods: wine and cheese
  • Notation for Unit labor req for cheese: 
          o  alc (home),
          o alc* (foreign);
  • Notation for Unit labor req for wine:      
          o alw (home),
          o alw* (foreign)
  • Opportunity cost in cheese production vs wine production for each country is given by:
          o  Home: alc/alw
          o  Foreign: alc*/alw*
  • L = total labor for Home
  • L* = total labor for Foreign
  • Pc = price of cheese
  • Pw = price of wine
  • World price or relative price of cheese is given by Pc/Pw (note that relative price of cheese vs wine is not the same in concept as opportunity cost of cheese production vs wine; it is the rate of exchange between Home and Foreign for cheese and wine)
  • Qc = quantity of cheese produced in Home; Qc* = quantity of cheese produced in Foreign
  • Qw = quantity of wine produced in Home; Qw* = quantity of wine produced in Foreign
  • Relative quantity of cheese to wine in world market is given by: (Qc+Qc*)/(Qw+Qw*)
  • Profits again are ignored
  • Home  country is more efficient in wine and cheese production, thus has an absolute advantage in all production: its unit labor requirements for wine and cheese production are lower than those in the foreign country: 
          o alc < alc*  and  alw < alw*
          o alc /alw  <  alc* / alw* 

In our numerical example, the Unit labor requirements for home and foreign countries are as follows:

TABLE 1. UNIT LABOR REQUIREMENTS FOR CHEESE AND WINE



From the Table 1 above, the opportunity cost of each country in cheese production vs wine production is:

Home: alc/alw = ½, which means it takes 1 hour to produce 1 lb of cheese and it takes 2 hours to produce a gallon of wine, which also means for every hour of unit of labor in Home, a cheese gets produced but only ½ of a gallon of wine gets produced.

Foreign: alc*/alw* = 6/3, or 2/1 in reduced form, which means it takes 2 hours to produce 1 lb of cheese and 1 hour to produce a gallon of wine, which also means, for every hour of unit of labor in Foreign, a gallon of wine can get produced but only ½ a lb of cheese. 

Given the unit labor requirements for each good for each country, the opportunity cost also equally implies the internal trade offs being made in their respective domestic economies:

  • To produce 1 more unit (lb) of cheese in Home country, it must stop producing or give up ½ gallon of wine (see PPF of Home country in Fig 3-1, p.27 of Krugman book)
  • To produce 1 more unit (lb) of cheese in Foreign country, it must stop producing or give up 2 gallons of wine (see PPF of Foreign country in Fig 3-2, p.30 of Krugman book).
Thus, Home country’s opportunity cost in cheese production over wine (alc/alw) < Foreign’s opportunity cost in cheese production (alc*/alw*). 

This means Home country has comparative advantage in cheese production.

From Table 1 showing unit labor requirements for each country, it’s clear Foreign is inefficient in the production of both cheese and wine, but has a comparative advantage in wine production:  
     alw*/alc* < alw/alc
     using figures in our numerical example, => 3/6 < 2/1 

Now let’s look at Fig 3-3, the subject of J’s question. Let’s break up the graph into bits:

  • Horizontal axis: relative quantity of cheese  is given by the amount of cheese produced in Home and Foreign combined, Qc+Qc* vs amount of wine produced in Home and Foreign combined, Qw+Qw* yielding the ff equation: (Qc+Qc*)/(Qw+Qw*)
  • Vertical Axis: relative price of cheese is given by Pc/Pw. This is the rate of exchange between a pound of cheese and a gallon of wine.
  • The RD or relative demand curve is downward sloping because of substitution effects. Recall that the model has 2 goods  that could be substituted for each other. As the relative price of cheese rises vs wine, consumers will tend to purchase less cheese and more wine, so the RD for cheese falls vs relative price—hence the downward slope. 
  • RS or relative supply curve is a stepped curve with 2 horizontal sections and 1 vertical section:
* the 2 horizontal sections depict pre-trade levels of production for wine and cheese for Home and Foreign respectively where the world price is just equal to their  opportunity costs or domestic production trade-offs
         * the vertical section depicts the range of relative prices and quantity of cheese and wine that gets produced AND at which they are traded.
  • Fig 3-3 below shows the world market for cheese and wine connecting the 2 markets for both goods produced by both Home and Foreign



Table 2 shows the production decision for each level of relative price of cheese in the world market when evaluated against each country’s opportunity cost in cheese production.  For Pc/Pw < ½ and for Pc/Pw> 2, these are extreme cases and shall be ignored for convenience.

TABLE 2. PRODUCTION DECISION VS RELATIVE PRICE OF CHEESE



Going back to Fig 3-3 again, there are 3 possible outcomes for trade: Pt 1, Pt 2, and Pt 3.
  • Pt  2 and Pt 3 are pre-trade levels where both Home and Foreign produce both cheese and wine making use of their own internal opportunity costs
  • Pt  1 is a convergent, equilibrium and optimal point of production where both countries specialize and trade their output.
Again, my student J’s question was:

Why wouldn’t Home and Foreign trade at Pt 2?

The answer is, Pt 2 is a possible outcome as with Pt 3 but is neither optimal nor an equilibrium/convergent point for the ff reasons:
  • At Pt 2, only Q’ relative amount of cheese gets produced, which is less than < (L/alc/L*/alw*) or the relative quantity of cheese produced WITH trade, or less cheese than what could have been produced under trade. Thus, from a world production standpoint, this is an INEFFICIENT POINT.
  • At Pt 2, Home produces both wine and cheese and Foreign is specializing in wine (See Table 2 for production decisions vs opp costs). Thus at Pt 2, Home is ‘possibly’ producing only sufficient for its domestic consumption. 
  • Suppose at Pt 2 both Home and Foreign DO have a chance to trade, the world price of cheese is 1/2 or the relative price of cheese is 1 lb for 2 gallons of wine. At this price level, Foreign will not have an incentive to trade because the world price implies wine is too cheap and cheese too expensive. Stated differently, at this price level, Foreign’s 1 hour of labor used to produce 1 gallon of wine, could be exchanged for ½ lb of cheese only. Thus, Foreign will ‘not likely’ engage in trade at Pt 2 and will seek a level such as Pt 1 where its 1 hour unit of labor producing 1 gallon of wine could be exchanged for a bigger amount: 1 lb of cheese--which makes more economic sense to Foreign.
  • Does it make economic sense to Home to produce and trade at Pt 1 too? Yes. By specializing in cheese production, Home can produce for domestic consumption and sell the rest to Foreign at a world price (Pc/Pw) of 1 or 1 lb cheese for 1 gallon of wine. By specializing in cheese and trading at Pt 1, Home is in a way indirectly producing wine at an opportunity cost of 1 is to 1 (or 1 lb of cheese to 1 gallon of wine), which is lesser than its actual, internal opportunity cost of 2/1.
Thus both Home and Foreign will seek and converge at Pt 1, which is not only efficient (more cheese being produced for same level of resources), but also optimal (best for Home and Foreign where they could trade their 1 hour unit of labor producing 1 good for a higher/bigger amount or a better relative or exchange price for their respective products). When economic actors ‘converge’ at a point and persist at this level, then this is the equilibrium point.  :)