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The handmade snuffbox industry is composed of 100 identical firms, each having short – run total costs given by STC = 0.5q2 + 10q + 5 and short – run marginal costs 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 will be the equilibrium in this marketplace? What will each firm’s total short – run profits be?
c) Graph the market equilibrium and compute total short – run producer surplus in this case.
d) Show that the total producer surplus you calculated in part c is equal to industry profits plus industry short – run total fixed costs.
e) Suppose the government imposed a 3$ tax on snuffboxes in the industry described above.
i) How would this tax change the market equilibrium.
ii) How would the burden of this tax be shared between snuffbox buyers and sellers?
iii) 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 do not fixed costs enter into computation of the change in the short-run producer surplus?
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