Intermediate Microeconomics and Its Application 12th Edition by Walter Nicholson,Christopher Snyder

Exercise 30

The handmade snuffbox industry is composed of 100 identical firms, each having short-run total costs given by
STC = 0.5q 2 + 10q + 5 and short-run marginal costs given by SMC = q + 10
where q is the output of snuffboxes per day.
a. What is the short-run supply curve for each snuffbox maker? What is the short-run supply curve for the market as a whole?
b. Suppose the demand for total snuffbox production is given by
Q = 1,100 - 50P
What is the equilibrium in this marketplace? What is each firm's total short-run profit?
c. Graph the market equilibrium and compute total producer surplus in this case.
d. Show that the total producer surplus you calculated in part c is equal to total industry profits plus industry short-run fixed costs.
e. Suppose now that the government imposed a $3 tax on snuffboxes. How would this tax change the market equilibrium?
f. How would the burden of this tax be shared between snuffbox buyers and sellers?
g. Calculate the total loss of producer surplus as a result of the taxation of snuffboxes. Show that this loss equals the change in total short-run profits in the snuffbox industry. Why don't fixed costs enter into this computation of the change in short-run producer surplus?