Question One [10 marks]

A firm produces cellular telephone service using equipment and labor. When it uses E

machine-hours of equipment and hires L person-ours of labor, it can provide up to Q

unites of telephone service. The relationship between Q, E, and L is as follows:

Q = EL . The firm must always pay PE for each machine-hour of equipment it uses and

PL for each person-hour of Labor it hires. Suppose the production manager is told to

produce Q=200 units of telephone service and that she wants to choose E and L to

minimize costs while achieving that production target.

a) What is the objective function for this problem? (2.5m)

b. What is the constraint? (2.5m)

c) Which of the variables (Q, E, L, PE, PL) are exogenous? Which are endogenous?

Explain. (2.5m)

d) provide a statement of the constrained optimization problem (2.5m)

Question Two [10 marks]

Suppose the demand for lychees is given by the following equation:

Qd = 4000 - 100P + 500PM , where P is the price of lychees and PM is the price of mangoes.

a) What happens to the demand for lychees when the price of mangoes goes up? Are

lychees and mangoes substitutes or complements? (2m)

b) Graph the demand curve for lychees when PM = 2.

Now suppose that the quantity of lychees supplied is given by the following equation:

Qs = 1500P - 60R , where R is the amount of rainfall. (2m)

c) On the same graph you drew for part b, graph the supply curve for lychees when

R = 50. Label the equilibrium price and quantity with P* and Q* respectively.

d) Calculate the equilibrium price and quantity of lychees. (2 m)

e) At the equilibrium values, calculate the price elasticity of demand and the price

elasticity of supply. Is the demand for lychees elastic, unit elastic, or inelastic? Is the

supply of lychees elastic, unit elastic, or inelastic? (1m)

f) At the equilibrium values, calculate the cross-price elasticity of demand for lychees

with respect to the price of mangoes. What does the sign of this elasticity tell you

about whether lychees and mangoes are substitutes or complements? (Hint: Check

to make sure that your answer is consistent with your answer to part a.) (1m)

Question Three [10 marks]

Aunt Joyce purchases two goods, perfume and lipstick. Her preferences are represented

by the utility function

U(P, L) = PL , where P denotes the ounces of perfume used and L denotes the quantity of lipsticks

used. Let PP denote the price of perfume, PL denote the price of lipstick, and I denote Aunt

Joyce's income.

a) Write out the consumer's utility maximization problem. (2m)

b) Derive her demand for perfume. Your answer should be an equation that gives P as

a function of PP , PL , and I. Determine this by using calculus and maximizing the

objective function, do not use the tangency condition. (4m)

c) Derive her demand for lipstick. Your answer should be an equation that gives L as a

function of PP , PL , and I. (Hint: look for symmetry between L and P). (2m)

d) What can be said about her cross-price elasticity of demand of perfume with respect

to the price of lipstick? (2m)

Question Four [10 marks]

A firm uses the inputs of fertilizer, labor, and hothouses to produce roses. Suppose that

when the quantity of labor and hothouses is fixed, the relationship between the quantity of

fertilizer and the number of roses produced is given by the following table:

Tons of fertilizer /month No of roses/ month

0 0

1 500

2 100

3 1700

4 2200

5. 2500

6. 2600

7. 2500

8. 2000

(Hint, write out the average and marginal product for each ton of fertilizer)

a) What is the average product of fertilizer when 4 tons are used? (2m)

b) What is the marginal product of the sixth ton of fertilizer? (2m)

c) Does this total product function exhibit diminishing marginal returns? If so, over

what quantities of fertilizer is it diminishing? (2m)

d) Does this total product function exhibit diminishing total returns? If so, over

what quantities of fertilizer is total product diminishing? (2m)

e) What is the efficient level of output it must produce at? (2m)

Question Five [10 marks]

Consider an island with exclusive fishing rights to their own waters. The fishing industry is

unregulated and the production function, representing the yearly catch, is given by

f (x) = 22x - x 2 /40 where is the number of boats launched. Yearly industry profit is split equally

among fishing boats and the cost of launching a boat equals 80. Fish is sold at a world market price

of p=40. A market failure is likely to occur in this market. Explain why and analyze the problem by

comparing the profit maximizing solution for the fishing industry with "sustainable" fishing

(revenue maximizing solution) and the free entry solution. Suggest a policy that leads to an efficient

outcome.

Question Six [ 10 marks]

A monopolist faces two totally separated markets with inverse demand p=100 - qA and

p=1602qB respectively. The monopolist has no fixed costs and a marginal cost given by mc= 2 /3

q Find the profit maximizing total output and how much of it that is sold on market A and market

B respectively if the monopoly uses third degree price discrimination.

a) What prices will our monopolist charge in the two separate markets? (6 m)

b) Calculate the price elasticity of demand in each market and explain the intuition behind the

relationship between the prices and elasticities in these two separate markets.