Consider a multiproduct firm that has a monopoly in the production of each of two goods. Suppose the demand functions are given by:

D1

(p1

, p2

) = 100

– 2p1

– p2 D2

(p1

, p2

) = 200

– p1

– 4p2 The total cost functions for production of each of the two goods are given by:

c1

(q1

) = 2q1 c2

(q2

) = 4q2

(a) Are these two goods substitutes or complements? Explain.

(b) Suppose the firm ignores the relationship between the two goods and uses the inverse elasticity formula to set the prices of the two goods as a markup over marginal cost. Calculate p1 and p2

.

(c) Now suppose that the firm takes into account the relationship between the two goods and sets the prices accordingly. Determine p1 and p2

. Are the prices higher or lower than the prices using the inverse elasticity rule? Explain the reason for your answer.

(d) Show that total profit is higher for the optimal prices than it is for the prices using the inverse elasticity rule.