In: Economics
Imperfect Competition — End of Chapter Problem
Suppose that the inverse market demand for pumpkins is given by ?=$10−0.05?. Pumpkins can be grown by anybody at a constant marginal cost of $1.
a. If there are lots of pumpkin growers in town, so that the pumpkin industry is competitive, what will be the equilibrium price (P), and how many pumpkins (Q) will be sold?
P = $
Q =
b. Suppose that a freak weather event wipes out the pumpkins of all but two producers, Linus and Lucy. Both Linus and Lucy have produced bumper crops and have more than enough pumpkins available to satisfy the demand at even a zero price. If Linus and Lucy collude to generate monopoly profits, how many pumpkins will they sell, and what price will they sell for?
Q =
P = $
c. Suppose that the predominant form of competition in the pumpkin industry is price competition. In other words, suppose that Linus and Lucy are Bertrand competitors. What will be the final price of pumpkins in this market—in other words, what is the Bertrand equilibrium price? At the Bertrand equilibrium price, what will be the final quantity of pumpkins sold by both Linus and Lucy individually and for the industry as a whole?
P = $
QLinus =
QLucy =
Qindustry =
d. In this scenario, Linus and Lucy will each earn
zero economic profits.
e. Suppose Linus lets it be known that his pumpkins are the most orange in town, and Lucy lets it be known that hers are the tastiest. The results you found in parts c and d would continue to hold to the extent that customers are
willing to substitute Linus's and Lucy's pumkins for one another.
f. Suppose Linus could grow pumpkins at a marginal cost of $0.95. What would be Linus's price and quantity? (Hint: assume Linus will price his product so as to undercut Lucy by the least amount possible.)
PLinus = $
QLinus =
g. In this scenario, Lucy's output would
fall to zero.