Part -1:

Be sure to explain your answers. A grade of zero is applied to unexplained answers.

1. Given two prospects with the same expected value and with the help of a diagram, determine whether a risk-averse individual prefers the prospect with the smaller spread in the outcomes. Answer the same for a risk lover.

2. Clarence makes his choices by maximizing expected utility. Clarence is risk averse.

(a) Clarence's friend Simon has offered to bet him $1000 on the outcome of the toss of a coin. If the coin comes up heads, Clarence must pay Simon $1000. If the coin comes up tails, Simon must pay Clarence $1000. If Clarence does not accept the bet, he will have $10,000 with certainty. Explain why Clarence refuses to take the bet. Illustrate this in a utility/wealth diagram.

(b) Simon would like to entice Clarence to take the bet. If Clarence's utility function is given by U(x)=√x, what is the minimum amount that Simon must pay Clarence to take the bet?

3. Consider the following production function: Q = L^1/2 + 5K^2/3.

What is the average product of labour, holding capital fixed?
What is the marginal product of labour?
Determine whether the production function exhibits diminishing marginal productivity of labour.
Determine the marginal rate of technical substitution.
What returns to scale does the production function have?

4. A Montreal firm uses labour to produce a commodity according to a production function f(L)=4√L. The commodity sells for $P per unit and the nominal wage paid to workers is $W.

(a) Determine the labour demand function from the profit maximization problem for the firm. Graph the labour demand function as a function of the real wage.
(b) Suppose that currently the firm is employing 12 workers when the price of the commodity is $100 and the nominal wage paid to workers is $50. Should the firm hire more workers, less workers, or keep its labour input the same?
(c) We can think of the number "4" in the production function as representing factors affecting the productivity of labour. Suppose that improvements in technology shift the production function. Show that this would shift the labour demand function as well.

5. A small firm produces a good using two inputs, labour (L) and machines (K). Her production function is f(L, k) = 6L^1/2 + 5K^2/3. Suppose that the wage rate is $100 per hour and the price of a machine is $25 per unit.

Suppose that the firm is currently employing a capital-labour ratio equal to 10. Is this the cost-minimizing capital-labour ratio? If it is, explain why it is. If it is not, explain what ratio the firm should employ. Illustrate the current position of the firm's production on a graph showing the isocost and isoquant and indicate where this current position is relative to the cost-minimizing position.
Find the amounts of labour and capital that will produce 120 units at minimum cost.

6. Consider the following cost function: TC(Q) = 2Q³ -4Q² + 6Q +3.

What is the total variable cost function?

What are the total fixed costs?

What is the average variable cost function?

What is the average fixed cost function?

What is the average total cost function?

What is the marginal cost function?

For what level of output is average variable cost a minimum?

What is the relationship between average and marginal cost?

Part -2:

1. Suppose that Home is a small country and its demand curve for a good is given by the demand curve: Q = 40 - 2P and supply of the good is given by the supply curve: Q = 2/3P.  The world price is 9. There is perfect competition in the market for this good.

(a) Determine the quantity consumed and supplied domestically if there is free trade.

(b) If the Canadian government imposes a tariff of $3, determine the Canadian price and level of imports.  How much revenue will the government earn from the tariff?  Determine the loss to consumers and the gain to producers. How large is the deadweight loss?

(c) If, instead, the government imposes an import quota of 8, what will the domestic price be?  What is the cost of the quota for Canadian consumers?  What is the gain for Canadian producers? What difference is there between the tariff and the quota?

(d) Now suppose the good is produced by a monopolist in the Home country. What difference would this pose for your answers to questions (b) and (c)? Note: you don't need derivations here. Simply explain and illustrate what is different.

2. Home's demand curve for wheat is Q=60-20P. Its supply curve is Q=20P-20. Foreign's demand curve for wheat is Q=80-20P and its supply curve is Q=20P-40.

(a) Determine which country will import wheat.

(b) Derive the import demand schedule and the export supply schedule.

(c) Determine the equilibrium world price of wheat and volume of trade.

3.  Following from problem 2, suppose that the importing country levies a specific tariff of 0.5 on wheat imports.

(a) Determine the effects of the tariff on (i) the price of wheat in each country, (ii) the quantity of wheat supplied and demanded in each country, and (iii) the volume of trade.

(b) Determine the effect of the tariff on the following groups: (i) import-competing producers, (ii) consumers in the importing country, and (iii) the government in the importing country.

(c) Determine the terms of trade gain in the importing country and the efficiency loss in the importing country.

(d) An optimal tariff is one that maximizes the net gains of a large country imposing an import tariff. Use this example to illustrate how an optimal tariff might be determined.

(e) Explain why imposing an import tariff is a beggar-thy-neighbour policy.

4. In comparison to question 1, suppose that the market for the good is supplied by a monopolist in the Home country in autarky. The marginal cost curve for the monopolist is MC = 3/2Q. The monopolist's demand curve is given by Q=40-2P and its marginal revenue curve is given by MR=20-Q.

(a) Illustrate and explain the quantity produced and the price in autarky.

(b) Now suppose that the country opens up to free trade. The world price is $9. Use a diagram to illustrate and explain what will be the quantity supplied domestically and the quantity imported.

(c) Explain why the outcome with trade is similar to the case when the domestic industry is perfectly competitive.

5.   A foreign monopolist selling in Home faces a demand curve given by P = 130-5Q. The firm's marginal revenue is given by MR = 130-10Q. The firm has a constant marginal cost of 10 per unit.

(a)    For the information given, determine the profit-maximizing output and price.

(b)   Suppose that the monopolist also sells its product in Foreign and it can price discriminate between the two countries. In Foreign, the demand curve is

      P = 190-3Q and the marginal revenue curve is MR = 190-6Q. Determine how  much the monopolist will sell in Foreign and what price it will charge. Explain  what determines which country is charged the higher price.

(c) Is the firm dumping?

6. In class, we examined the tariff game among large countries. Now consider the tariff game between a large country and a small country.

(a) Show the payoff matrix if the large country applies an optimal tariff.

(b) Determine the Nash equilibrium or Nash equilibria for this game.

(c) What does your answer to (b) tell you about the role of multilateral trade agreements such as with the WTO in a situation like this?

7. Suppose that two countries are currently negotiating a free trade area. The two countries currently have tariffs imposed on goods traded between them and between each of them and countries outside of the proposed free trade area. Will such an agreement benefit both countries?