Answer all questions.
Explanations can be brief.
100 points possible.
1) [36 points]
Suppose that, within the state of Wisconsin, market demand for cigarettes
is given by Q
= 570 – 57 P, while market supply is given by Q
= 400 P – 800, where P
is the price per pack (in dollars) and quantities are given in millions of packs.
(Throughout this question, the market for cigarettes is assumed to be perfectly
a) Compute the equilibrium price and equilibrium quantity.
Then compute consumer
surplus, producer surplus, and total surplus. [HINT: You are not required to draw graphs
for this problem, but they might help you compute the relevant amounts.]
b) Suppose that the state of Wisconsin now imposes a tax of $2 per pack on cigarettes.
Find the new equilibrium price and quantity. Then compute consumer surplus (CS),
producer surplus (PS), the state’s revenue from the tax, and total surplus (TS).
Given the existence of a tax, TS = CS + PS + tax revenue.]
Comparing your answers to
parts (a) and (b), how has the tax affected total surplus?
Briefly discuss the concept of
“deadweight loss” and give the size of this loss in the current problem.
c) A state representative argues that, given the state’s projected budget shortfall, the
cigarette tax should be set even higher.
Compute the equilibrium price and quantity and
the state’s tax revenue if the tax is set at $4 per pack.
d) Using your answers to parts (a) and (b), compute the elasticity of demand as the price
moves from the initial price (in part a) to the higher price (in part b).
Then, using your
answers to parts (b) and (c), compute the elasticity of demand if the price rises again.
Are these elasticities the same? Briefly explain why or why not.
e) Arguably, cigarette taxes are imposed more for their long-run consequences than their
Qualitatively, how would the demand for cigarettes change in
the long run?
How would this affect the government’s tax revenue?
2) [24 points]
A firm produces output Q from labor input L according to the production
Q(L) = 20L – L
Derive the firm’s marginal-product-of-labor (MPL) function.
[HINT: You can either derive this function analytically using calculus, or you can
construct a table that gives the firm’s MPL for various levels of L.]
that the firm’s output sells at a price of $3 per unit, derive the firm’s value-of-marginal-
[HINT: Again, you can derive this function analytically, or
else add another column to your table.]
What is the relationship between the firm’s
value-of-marginal-product-of-labor function and its labor-demand function?
graph of the firm’s labor demand curve.
If the wage is $12 per unit of labor, what is the
optimal level L* chosen by the firm?
Given this (optimal) choice of labor, find the total
revenue, total cost, and profit earned by the firm.