Handout 2: Answers Exercise 1 A part of the answer can be found in Markusen J. R., Melvin J. R., Kaempfer W. H., Maskus K. E., (1995), International Trade: Theory and Evidence. Subsidia is a small open economy lying in the South Pacific. It produces two good Y, which is capital intensive and X, which is labor intensive. The close economy general equilibrium of Subsidia is represented as point A in the diagram below. Foreword: The slope of the transformation curve and indifference curve. Begin with the supply side and recall from your micro class that tha value of the marginal product of a factor is the price of the good times the physical marginal product of the factor. In a 2 industries, 2 factors economy, the competitive equilibrium involves four of these condition, two factors for each of two industrie. Let MPLX be the marginal product of the labor in industry X
and define the other marginal product similarly, then :
By dividing the top equations by the lower equations, and rearranging wefind:
The marginal products are the change in the relevant output divided by thechange in the relevant input (MPLX dX ). Using these relationships, we
But because factor are in fixed total supply dLX "dLY and dKX "dKY.
We can then reduce equation 3 to a simple expression:
where MRT stands for the Marginal Rate of Transformation (Note that dY
and dX must have the opposite signs so that the MRT is positive. If factor andcommmodity markets are competitive and if industries face the same factor prices, thenproduction will occur at a point where the commodity price ratioproduction frontier. Now on the demand side, the utility is maximized by setting the marginalrate of substitution equal to the ratio of commodity price.
The Autarky general equlibrium requires that the two optimization conditionsfor the consumer and producer are satisfied and that the supply anddemand for each commodity are equal (Market Clearing):
p PX MRS MRT
The Figure below show the equilibrium for the closed economy
Derive the new general equilibrium when free trade is allowed andSubsidia partially specialized and export good Y.
Subsidia engages in Trade at a fixed world price ratio p' pX
economy is no longer constrained to consume only what it produces. Instead of the market clearing condition (equation 10), we use the tradebalance condition that states that the value of all the imports equal the valueof all the exports:
XXc " XppYYc " Yp 0
Subsidia specialized in export the commodity Y, the new world trade
equilibrium is depicted in the folowing graph:
Assume the Subsidian government imposes an export subsidy ongood Y. Draw the implication of this policy in the diagram. What isthe impact of this policy on the national income, trade (export,import) and Welfare?
Suppose that s is as ad valorem subsidy rate on exports of Y. ThenpY pY1 s and p p'. The new general equilibrium requires
XXc " XppYYc " Yp 0
The export subsidy causes the country to produce more Y than X than at the
free trade equilibrium. Subsidia produces now at Qs specializing more in the
good in which it has a comparative advantage. Consumption occurs now atCs where the MRS in consumption equals the distorted domestic price ratio.
The real national income ONs is smaller than in free trade as indicated in
the diagramm above: ONs ONf. The country trade more (both import and
export increases) but welfare is reduced from Uf to Us. Note that export
subsidies are usually more welfare-decreasing than tariffs because theyrequire taxpayers to fund them, rather than generating tax revenues.
What does the export subsidy implies for the distribution ofincome?
The Stolper-Samuelson theorem set that if there are constant returns toscale and if both commodities continue to be produced, a relative increasein the price of a commodity will increase the real return to the factor usedintensively in the industry and reduce the real return to the other factor. Good Y is capital intensive so that the increase of the price of Y through the
subsidy increases the real return to capital and reduce the real wage.
How would your answer change if capital was to be sector specific?
consider the figure below with 4 quadrants:
Quadrant III shows the total quantity of labor available to the two
Quadrants II and IV: The marginal product curves (slope of the total
product curves). They slope downward because we assume the totalproduct curve to be concave (diminishing returns to scale).
The distance OM in the diagram, which is the marginal product of labor in Y,gives the real return to labor for workers in Y. (The same can be derived forOM’, the real return to labor in the X industry)
p and MPX w , the slope of the line MM’ is PX .
Note also that since OM and OM’ are the real return to labor respectively inY and X, the line MM’ is the budget constraint for a representative worker. What does happen when the price of Y increase?The new budget constraint for our representative worker is given by NN’. The marginal product of labor has fallen from OM to ON in the Y industryand risen from OM’ to ON’ in the X industry. Thus the welfare of therepresentaitve consumer will depend on the consumption pattern. Ingeneral, the effect of a price change on the welfare of labor is uncertain anddepends on the preferences for the two commodities. This is in contrast tothe HO model where the change in commodity price has an unambiguouseffect on factor prices. How have the returns of the specific factors been affected by the relative increase in theprice of Y?
In the Y industry, the marginal product of capital must increase since
the marginal product of labor has fallen from OM to ON.
In the X industry, the marginal product of labor has risen from OM’ to
ON’. The marginal return of capital in this industry must decrease.
Thus, a relative increase in the price of commodity Y produces a gain for the specific factor used to produce Y and reduce the income of the specific factor used in industry X. Exercise 2 (from P. Krugman, M. Obstfeld, Chapter 8) Home’s demand curve for good Y is given by:
Foreign’s demand curve for good X is given by:
Derive and graph both Home’s import demand and foreign’s exportsupply schedule when tey are allowed to trade at zero transportcost. What is the world price? What is the volume of trade?
Suppose home impose a tariff of 0,5 on good Y imports.
Determine and graph the effect of tariff on the price andquantity of good Y.
Since the export supply and import demand lines are symetric, the burdenof the tariff fall equally on the two countries. Home’s price increases by 0,25to 1,75. Foreign’s price fall by 0,25 to 1,25. The volume of trade is now 10.
Determine the effect of the tariff on Welfare.
Home consumers incur a welfare loss as price rises. The loss in consumersurplus is equal to 16,875The welfare of import competing producers increases as the priceincreases. The producer surplus is 13,125Governement gains tariff revenue equal to 5
Show graphically and calculate the terms of trade gain, theefficiency loss and the total effect on welfare of the tariff.
The efficiency loss is equal to 1,25 The total welfare effect of the tariff is equal to 1,25 Exercise 3 (from P. Krugman, M. Obstfeld, Chapter 8) The Nation of Acirema is unable to affect world prices. It imports peanuts at the price of 10$ per bag. The demand curve is:
Determine the free trade equilibrium. Then calculate and graph thefollowing effects of an import quota that limits imports to 50 bags:

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