Answers to Textbook Problems - Chapter 8

1. The import demand equation, MD, is found by subtracting the home supply equation from the home demand equation. This results in MD = 80 - 40*P. Without trade, domestic prices and quantities adjust such that import demand is zero. Thus, the price in the absence of trade is 2.

2.a. Foreign's export supply curve, XS, is XS = -40 + 40*P. In the absence of trade, the price is 1.

b. When trade occurs export supply is equal to import demand, XS = MD. Thus, using the equations from problems 1 and 2a, P = 1.50, and the volume of trade is 20.

3.a. The new MD curve is 80 - 40 * (P+t) where t is the specific tariff rate, equal to 0.5. (Note: in solving these problems you should be careful about whether a specific tariff or ad valorem tariff is imposed. With an ad valorem tariff, the MD equation would be expressed as MD = 80 - 40*((1+t)p). The equation for the export supply curve by the foreign country is unchanged. Solving, we find that the world price is $1.25, and thus the internal price at home is $1.75. The volume of trade has been reduced to 10, and the total demand for wheat at home has fallen to 65 (from the free trade level of 70) while the total demand for wheat in Foreign has fallen to 55.

b. and c. The welfare of the home country is best studied using the combined numerical and graphical solutions presented below in Figure 9-1.

(figure in answer book)

where the areas in the figure are:

a: 55(1.75-1.50) - .5(55-50)(1.75-1.50)=13.125

b: .5(55-50)(1.75 - 1.50) = 0.625

c: (65 - 55)(1.75 - 1.50) = 2.5

d: .5(70 - 65)(1.75 - 1.50)=0.625

e: (65 - 55)(1.50 - 1.25) = 2.50

Consumer surplus change: -(a+b+c+d)=-16.875. Producer surplus change: a=13.125. Government revenue change: c+e=5. Efficiency losses b+d are exceeded by terms of trade gain e. [Note: in the calculations for the a, b and d areas a figure of .5 shows up. This is because we are measuring the area of a triangle, which is one half of the are of the rectangle defined by the product of the horizontal and vertical sides.]

4. Using the same solution methodology as in problem 3, when the home country is very small relative to the foreign country its effects on the terms of trade are expected to be much less. The small country is much more likely to be hurt by its imposition of a tariff. Indeed, this intuition is shown in the problem. The free trade equilibrium is now at the price $1.09 and the trade volume is now $36.40.

With the imposition of a tariff of 0.5 by Home, the new world price is $1.045, the internal home price is $1.545, home demand is 69.10 units, home supply is 50.90 and the volume of trade is 18.20. When Home is relatively small, the effect of a tariff on world price is smaller than when Home is relatively large. When foreign and home were closer in size, a tariff of .5 by home lowered world price by 25%, whereas in this case the same tariff lowers world price by about 5%. The internal Home price is now closer to the free trade price plus t than when Home was relatively large. In this case, the government revenues from the tariff equal 9.10, the consumer surplus loss is 33.51 and the producer surplus gain is 21.089. The distortionary losses associated with the tariff (areas b+d) sum to 4.14 and the terms of trade gain (e) is 0.819. Clearly, in this small country example the distortionary losses from the tariff swamp the terms of trade gains. The general lesson is the smaller the economy, the larger the losses from a tariff since the terms of trade gains are smaller.

5.

The Europeans produce an aircraft worth $50 million, with $30 million of imported inputs. Hence, if there were no subsidy, the European value-added (contribution) to the aircraft production would be $20 million.

The governments provide a $10 million subsidy for each aircraft. This allows the industry to cash a value-added of $30 million.

Hence the effective rate of protection is:

(30 - 20) / 20 = 50%

6. We first use the foreign export supply and domestic import demand curves to determine the new world price. The foreign supply of exports curve, with a foreign subsidy of 50% per unit, becomes XS = -40 + 40(1+0.5) *P. The equilibrium world price is 1.2 and the internal foreign price is 1.8. The volume of trade is 32. The foreign demand and supply curves are used to determine the costs and benefits of the subsidy. Construct a diagram similar to 8.11 in the text and calculate the area of various polygons. The government must provide (1.8 - 1.2) * 32 = 19.2 units of output to support the subsidy. Foreign producers surplus rises due to the subsidy by the amount of 15.3 units of output. Foreign consumers surplus falls due to the higher price by 7.5 units of the good. Thus the net loss to Foreign due to the subsidy is 7.5 + 19.2 - 15.3 = 11.4 units of output. Home consumers and producers face and internal price of 1.2 as a result of the subsidy. Home consumers surplus rises by 70 * .3 + .5(6 *.3) = 21.9 while Home producers surplus falls by 44 *.3 + .5(6*.3) =14.1, for a net gain of 7.8 units of output.

7. At a price of $10 per bag of peanuts, Acirema imports 200 bags of peanuts. A quota limiting the import of peanuts to 50 bags has the following effects:

a.) The price of peanuts rises to $20 per bag.

b.) The quota rents are ($20 -$10)*50 = $500.

c.) The consumption distortion loss is .5*100 bags*$10 per bag = $500.

d.) The production distortion loss is .5 *50 bags *$10 per bag = $250.