1. * Suppose that the marginal cost faced by Sketchers is a constant $10 per pair
of shoes. If the demand elasticity for Sketchers shoes is also constant and is
equal to 5, what price should Sketchers charge per pair of shoes?
2. Suppose there are only two firms in an industry selling an identical product
where the quantity produced and sold can change rapidly. Discuss why the
prisoneràdilemma is likely to be faced by these oligopolists when they decide
on the prices to set. Discuss why it is in the interest of society to prevent the
two firms from colluding and setting one price for their good.
3. Suppose there are only two firms in an industry selling an identical product
where the quantity produced must be set well in advance of the good being
sold in the market (and thus the quantity cannot be changed rapidly). The
market demand for this good is given by the following equation: Q = 1,000 ´P. Firm Aàmarginal cost of production is as follows: MCA = 30 + 1.5QA. Firm
Bàmarginal cost of production is as follows: MCB = 100 + 2.5QB. Assume that
each firm knows the otheràcost of production.
a. If the two firmàdecide their output simultaneously, how much output will
each firm produce? What price will be charged in the market for the
good?
b. If the firm Aàdecides its output first and then B decides its output second,
how much output will each firm produce? What price will be charged in
the market for the good? Does A have an advantage by setting output
first? Explain.
4. * Two companies each own property (and mineral rights) in an oil field. Each
firm therefore has the legal right to drill for oil on its land and take out as much
oil as it can. The problem, of course, is that one companyàactions affect how
much oil the other can produce. The following matrix represents how each of
these companies view the situation. The terms outside the matrix represent
oil output by each firm (low, medium, or high), while the numbers in each cell
show the present value of all oil to be extracted by each company, given the 2
extraction policies. The first number represents the value to Company A and
the second number represents the value to Company B. As an example, if
Company A pumps at a /w2ate, and Company B pumps at a /w2ate, then
the value to Company A of all the oil it expects to take over the life of the field
is $100 while the value to Company B of its oil is $8.
Low
Company A’s
Medium
Extraction Rate
High
Company B’s Extraction Rate
Low
Medium
High
100, 8
80, 15
50, 30
125, 5
110, 10
55, 22
120, 3
115, 8
60, 20
a. What extraction rates maximize the total value of the oil field?
b. Does the set of extraction rates of part (a) represent a stable situation?
Explain.
c. Is there a dominant strategy (extraction rate) for either or both players?
Explain.
d. Is there a Nash equilibrium set of extraction rates? If so, does it maximize
the total value of the oil field?
e. Is there a mutually beneficial exchange inherent in this matrixîe that
could solve the problem these 2 companies face? If Company A were put
purchase Company Bàoil rights, how much would it have to pay? Is this a
feasible transaction?

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