Ali (A), Beth (B), and Carlos (C) are the only producers of a commodity called Panic- Aid, which is in great demand in 5110land. Each producer can produce Panic-Aid according to a cost function:
C(yi) = 0.5 yi2
where i = A, B, or C. Note that there are no fixed costs. The three firms act as perfect competitors.
(a) What is the marginal cost function for each producer?
(b) If Panic-Aid sells for a price of p per unit, how many will each of them produce?
(c) At a price of p, how many Panic-Aids will be supplied on the market?
The demand function for Panic-Aid is: D(p) = 16 - p (d) Find the equilibrium price and quantity of Panic-Aid (e) How much profit does each producer earn?
(f) How do you reconcile positive profits (in part (e)) with the assumption that Ali, Beth and Carlos are perfect competitors?
(g) Draw a single diagram showing demand function for Panic-Aid. aggregate supply [obtained in (c)] equilibrium price and quantity consumer surplus
(h) Suppose Ali, Beth and Carlos merge to become a monopoly firm ABC. If they wish to produce Y units how much would they choose to produce in eachplant?Thatis,whatareyA,yB andyCif yA +yB +yC=Y?
(i) Assuming monopoly structure, determine the equilibrium
a. price and quantity b. Consumer surplus and profits c. Deadweight loss