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! :)