Part I

1.a Assume that a person’s utility function is given by the following function: TU = 36X − 2X2  + Y

Assume also that the price of X is £8, and the price of Y is £1 and that the budget is £70. What is the optimal amount of goods X and Y that should be purchased with this budget?

1.b Assume now that the price of good X is PD , while all other conditions remain the same.  Find the optimal amount of good X that should be purchased for a generic price PD . In other words, find the individual demand function for good X.

2.a Assume that a firm is operating on a perfectly competitive market with a market price of

12. The firm faces the following average cost function: AC =  + 6 + 3Q

What is the optimal amount of good that should be produced by this firm?

2.b Assume now that the price of the good is PS , while all other conditions remain the same. Find the optimal amount of the good that should be produced by this firm for a generic price PS . In other words, find the individual supply function for this good.

3.a Assume there are 40 identical consumers with the demand function you found in question 1.b and 60 identical firms with the supply function you found in question 2.b. Find the equilibrium market price and quantity.

3.b Assume that instead of 60 firms there is just one firm operating as a monopolist. Discuss how the market equilibrium would change and how you would find the equilibrium (you do not need to solve for the equilibrium).

4.a Assume that the government introduces a subsidy of 2 per unit of good sold. Find the new market equilibrium.

4.b Discuss how the subsidy is distributed between the consumers and the producers (you do not need to solve for it). In your discussion, focus on the effect of the elasticities on the distribution.