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Problem_Set_2_solutions

Problem_Set_2_solutions
Problem_Set_2_solutions

AP/ECON3150International Trade

Problem set2Solutions

Problem1

Canada and U.S.trade two products with each other-Automobiles(A) and Cloth(C).Each product is produced using labour only but there are two types of workers in each industry:Skilled(S)and Unskilled(U).Unskilled workers can easily change occupation and move from one industry to another if they can earn more there.Skilled workers,however,cannot change occupa-tion because their skills are speci…c to the industry in which they work.For example,in the clothing industry there is no demand for skilled mechanics who spent most of their lives assembling https://www.wendangku.net/doc/6a6425367.html,ing classroom terminology, U is a mobile factor of production,while S A and S C are‘speci…c factors’-a skilled auto worker can only work in Automobile industry,and a skilled clothing worker can only work in a clothing industry.Both auto and clothing industries experience diminishing returns to each type of labor.Also assume that Canada is relatively better than U.S.in producing cars.

a.Draw a PPF diagram for Canada.Justify its shape and compare it to the U.S.PPF.Put cars on horizontal axis.

Answer:

The PPF for Canada is bowed-out.Point C1shows the maximum possible output of cloth if all unskilled workers move to cloth industry,and A1shows the maximum output of cars if all unskilled workers work in auto industry. (Note that at A1the output of cloth does not need to be zero since skilled

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workers can still produce positive output of cloth.However,this is not critical for our problem).The closer the economy is to point C1,the lower is the productivity of unskilled labor in cloth and the higher it is in Auto.As more U labor is added to the production of cloth,the marginal product of U labor declines so that although the output of cloth continues to increase,the output is increasing at a decreasing rate.So the opportunity costs of cloth are going up(and opportunity costs of cars are going down)the closer we are to C1.As a result,PPF gets?atter as we move closer to C1.

Since Canada is assumed to be more productive in cars,its PPF will be ?atter(skewed towards cars)than the U.S.PPF.

b.Assume that preferences of Canadian and U.S.consumers are rep-resented by some indi¤erence curve U(same for both countries):Draw two diagrams that show Canadian and U.S.no-trade equilibrium,i.e.equilib-rium output and consumption of each good and equilibrium relative prices. Explain how to…nd equilibrium relative https://www.wendangku.net/doc/6a6425367.html,pare Canadian and U.S. relative prices.

Answer:without trade equilibrium will be at on the PPF where it is tangent to utility curve(E can for Canada and E us for the U.S.)This tangency condition ensures that utility of consumers is maximized subject to resources available in the economy.At this point the slope of the tangency line to both PPF and U will be equal to OC A at the equilibrium and,therefore,to the equilibrium relative price of cars p A p C 0in order for the zero-pro…t condition to be satis…ed in both

industries.

c.Suppose that once Canada started to trade with the U.S.,the equi-

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librium price of cloth,p T C ,has decreased relative to no-trade price,while

the price of cars remains the same.This implies that p T C p T A

Canada export?Illustrate gains from trade.

Answer:When the relative price of cloth goes down,the relative price of cars is going up and the new (trade)equilibrium production in Canada will be at point P ,where the new price line p A p C

T is tangent to the Canadian PPF.Q P A cars and Q P C cloth are produced.Given these output levels and market

prices,consumers would be willing to purchase Q C A cars and Q C C units of cloth (point C ).Therefore, Q P A Q C A >0number of cars Canada would export to the U.S.and Q C C Q P C >0yards of cloth Canada would import from

the U.S.

When domestic consumption moves from E 0to C ,the utility associated with the new consumption level increases.Consumers’utility rises from U 0to U 1.This increase re?ects gains from trade to an average Canadian

consumer.

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https://www.wendangku.net/doc/6a6425367.html,e a diagram similar to Figure3.8on p.26of the class notes(Class

3)to illustrate the e¤ect of trade on the wage rate of unskilled workers.How does trade a¤ect real earnings of unskilled workers?

Answer:The diagram below shows Canadian labor market before and after trade.We measure unskilled labor(mobile factor)on the horizontal axis.The no-trade unskilled labor market equilibrium is at point E0.At that point wage of unskilled worker in each industry is the same and equals to W A, the value of the marginal product of unskilled labor in each industry,so there is no reason for unskilled workers to change occupation.The decrease in the price of cloth shifts the p C MP UL C curve down to p T C MP UL C so that the new equilibrium is at point E T.The number of unskilled workers employed

in auto industry increases from O A L A to O A L T

A ,although the amount of

labor devoted to cloth decreases from O C L A to O C L T

A .The nominal wage

falls from W A to W T,but the decrease is less than the vertical shift of the p C MP UL C curve given by p C p T C MP UL C so the nominal wage falls by less than price of cloth and hence real wage of unskilled workers measured in the units of cloth will increase:W

p C"

Also,the nominal wage has decreased while the price of cars was assumed to remain at the pre-trade level.Therefore,real wage of unskilled workers measured in the units of cars has decreased as well:W

p A#

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f.What is the impact of trade with the U.S.on earnings of skilled workers in Canadian auto and clothing industries?

Answer:Denote wage of skilled workers in auto industry with W SA and in clothing industry with W SC .Because skilled workers are limited in their opportunities to change industrial occupation,skilled workers in auto industry (exported product)will gain from a decrease in p C ;while real earnings of skilled workers in clothing industry in Canada would fall.This is because reallocation of unskilled workers from clothing to auto makes skilled workers in auto industry more productive (MP SL A "),therefore from W SA =

p A MP SL A we obtain that W SA ",W SA p A =MP SL A ".The real wage in terms of cloth also has increased W SA p C " since nominal wage has increased while p C has decreased.Therefore,real earnings of skilled workers in car

industry is greater under free trade.

The opposite is true for skilled workers in clothing.Since unskilled work-ers leave clothing industry when p C #,skilled labor productivity in clothing would fall and W SC =p C MP SL C #.Since p C is higher under trade,we obtain that W SC p C =MP SL C #,and W SC p A also falls because W SC fell while p A is constant.Therefore,the real income of skilled workers in clothing industry (import-competing)would decrease under free trade with the U.S.Problem 2

In the gains from trade diagram (Class3,Figure 3.6on p.19),suppose that instead of having a rise in the relative price of manufactures,there is a fall in that relative price.

a.Starting at the autarky point (‘No-trade production and consumption),show what would happen to production and consumption.

Answer:

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As seen in the diagram,a fall in the relative price of manufactures is shown by the smaller slope(in absolute value)of the international price line. The country produces at point B now,at which the international price line is tangent to its PPF.The higher relative price of agriculture attracts workers into that sector such that the output of agriculture increases and the output of manufactured goods decreases.Now the highest level of utility is achieved where the highest possible indi¤erence curve intersects with the new price line(at C).The increase in utility signi…ed by the higher indi¤erence curve is

a measure of gains from trade.

b.Which good is exported and which is imported?

Answer:The decrease in the relative price of manufactures in the trade equilibrium(compared with autarky)also means that the country has com-parative advantage in agriculture and is,therefore,importing manufactured goods and exporting agricultural goods.

c.Explain why the overall gains from trade are still positive.

Answer:Overall gains from trade are still positive because the country is able to sell agriculture at a higher price and buy manufactured goods at a lower price than it could have in autarky.The fact that the relative price (of manufactured goods)fell with trade indicates that the foreign country’s autarky relative price was lower.That is,in this case the country has a comparative advantage in agriculture.

Problem3

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Suppose two countries,Canada and Mexico,produce two goods,timber and televisions.Assume that land is speci…c to timber,capital is speci…c to televisions,and labor is free to move between the two industries.When Canada and Mexico engage in free trade,the relative price of televisions falls in Canada and the relative price of timber falls in Mexico.

a.In a graph that shows labour market equilibrium(similar to Figure3.8 on p.26,Class3),show how the wage changes in Canada because of a fall in the price of televisions,holding constant the price of timber.Can we predict the change in the real wage?

Answer:As shown by the following…gure,real wage falls but by less than the percentage decrease in the price of televisions.This implies that real wages measured in televisions has increases,while real wage measured in timber has decreased.

b.What is the impact of opening trade on the rentals on capital and land in Canada?Can we predict that change in the real rentals on capital and land?

Answer:Because capital is speci…c to the television sector,the drop in the relative price of television will lead to a fall in the rental on capital.With Canada exporting timber,rental on land will rise because land is speci…c to the timber industry.

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c.What is the impact of opening trade on the rentals on capital and land in Mexico?Can we predict that change in the real rentals on capital and land?

Answer:Through the exports of televisions,the relative price of tele-visions will rise in Mexico,which will lead to an increase in the rental on capital.By contrast,the rental on land will fall.

d.In each country,has the speci…c factor in the export industry gained or lost,and has the speci…c factor in the import industry gained or lost?

Answer:In both cases,the speci…c factor in the export industry(i.e., land in Canada and capital in Mexico)gained whereas the factor speci…ed to the import industry(i.e.,capital in Canada and land in Mexico)loses when the two countries engage in trade.

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