Question

Suppose that each firm that sells cases of jelly-beans has a cost function of C(q) = 25 + q²+q and that the market demand for jelly-beans is Q_D = 52 – 2∙P.

A) What is the short-run industry supply curve?

B) Suppose that in the interest of jelly-bean consumers, the government mandates that cases of jelly-beans can only be sold for $10. Use the short-run supply curve to find the dead-weight loss associated with this policy?

Answer 1

Marginal cost function will be the supply function

Supply:
P = dC/dQ = 2Q + 1
Qs = P/2 - 1/2

Govt Price = 10
Quantity demand = 52 - 2*10 = 32
Quantity supply = 4.5
As there is a shortage, only 4.5 units will be supplied
Consumer surplus (difference between maximum price and current price) = (25-10)*4.5
Producer (difference between minimum price and current price) = (10-1)*4.5
Price as per demand and supply
P/2 - 1/2 = 52 - 2P
2.5P = 52.5
P = 21
Q = 52 - 2*21 = 10
Consumer surplus (difference between maximum price and current price) = (25-21)*10
Producer (difference between minimum price and current price) = (21-1)*10

Deadweight loss = ((25-21)*10+(21-1)*10) - ((25-10)*4.5+(10-1)*4.5) = 132