1. The marketing of the Summers Company must formulate a recommendation
concerning the price to be charged for a new product. According to tile best
available estimates, the marginal cost of the new product will be 18 and the price
elasticity of demand for this product will be -3.0.
(1) What recommendation should she make if Summers wants to maximize
profit? (5 points)
(2) If her recommendation is accepted, what will be the new product's marginal
value? (5 points)
2. If the demand for diamonds is given by Pz= 980 - 2Q2, where Qz is the number of
the diamonds demanded if the price is Pz per diamond. The total cost (TCz) of the
De Beers Company (a Monopolist) is given by TCz = 100 +5QZ = 0.54z2, where
Qz is the number of diamonds produced and put on the market by the De Beers
Company, suppose that the government could force De Beers to behave as if it
were a perfect competitor: that is, via regulation, force the film to price Diamonds
at marginal cost.
(1) What is social welfare when De Beers acts as a single price n~onopolist?(5
points)
(2) What is social welfare when De Beers acts as a perfect competitor? (5 points)
(3) How much does social welfare increase when De Beers moves from
monopoly to competition? (5 points)
3. The Backus Corporation makes two products, X and Y. for every unit of good X
that the firm produces, it produces two units of good Y. Backus's total cost
~ Q
, is the number of units of output (where
function is TC = 500 + 3 4 + 9 ~where
each unit contains one unit of good X and two unit of good Y) and TC is total cost
(in dollars). The demand curves for the firm's two products are Px = 400- Qx and
Py = 300 - 3Qy, where Px and Qx are the price and output of product X and Py
and Qy are the price and output of product Y.
(1) How much of each product should the Backus Corporation produce and sell
per period of time? (5 points)
(2) What price should it charge for each product? (5 points)
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