Suppose there are 100 identical firms in the perfectly competitive cement industry. Suppose the cement industry is a Constant-Cost industry. Each firm has a short-run total cost function of the form: STC=.5q2+10q+8, and its short-run marginal cost is given by SMC=q+10, where q is the tons of cement per day. The market demand for cement is given by QD=1100-50P.
a) Find the short-run supply (QS) of the industry.
b) What is the market equilibrium P and Q?
c) Compute the consumer surplus (CS) and producer surplus (PS).
d) What is the firm’s profit maximizing output q? What is the firm’s profit?
For part e)-n), suppose that the government imposed a $2 per-unit tax on cement.
e) How would this tax affect each firm’s short-run marginal cost function?
f) How does this change the short-run supply (QS) of the industry?
g) What is the resulting market equilibrium P and Q?
h) What is the firm’s profit maximizing output q?
i) Is the firm making a profit or a loss after the per-unit tax? How much?
j) How much does the government collect in tax revenue?
In the Long-Run, all firms in the industry will make zero economic profit.
k) What is the firm’s profit maximizing output q in the long run?
l) What is the market equilibrium P and Q in the long run?
m) Are there entries or exits of the firms? What is the new market supply curve after the entries or exits of the firms?
n) What is the number of firms in the industry in the long run?