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Wyandotte currently sells 30,000 gallons of polyol per year at an average price of $15.00 per gallon. Fixed costs of manufacturing polyol are 90,000 per year and total variable cost equal 180,000. The operations research department has estimated that a 15% increase in output would not affect fixed costs but would reduce average variable costs by 60% per gallon. The marketing department has estimated the arc elasticity of demand for polyol to be -2.0.
How much would Wyandotte have to reduce the price of polyol to achieve a 15% increase in the quantity sold?
B. Evaluate the impact of such a price cut on (i) total revenue, (ii) total costs, and
(iii) total profits.
Chapter 12: Problems 1, 2(b), and 5(b)
1. Assume that two companies (C and D) are duopolists that produce identical products. Demand for the products is given by the following linear demand function:
P = 600 – QC – QD
where Qc and QD are the quantities sold by the respective firms and P is the selling price. Total cost function for the two companies are:
TCc = 25,000 + 100Qc
TCD = 20,000 + 125QD
Assume that the firms act independently as in the Cournot model (i.e., each firm assumes that the other firm’s output will not change).
A. Determine the long – run equilibrium output and selling price for each firm.
B. Determine the total profits for each firm at that equilibrium output found in Part (a).
2. Assume that two companies (A and B) are duopolists who produce identical products. Demand for the products is given by the following linear demand function:
p = 200 – QA – QB
Where QA and QB are the quantities sold by the respective firms and P is the selling price. Total cost function for the two companies are:
TCA = 1500 + 55QA + Q2A *A should be directly under the 2)
TCB = 1200 + 20QB + 2Q2B *B should be directly under the 2)
Assume that the firms act independently as in the Cournot model (i.e., each firm assumes that the other firm’s output will not change).
B. Determine the total profits for each firm at that equilibrium output found in Part (a).
5. Alchem (L) is the price leader in the polyglue market. All 10 other manufacturers (follower [F] firms) sell polglue at the same price as Alchem. Alchem allows other firms to sell as much as they wish at the established price and supplies the remainder of demand itself. Total demand for polyglue is given by the following function (QT = QL + QF):
P= 20,000 – 4QT
Alchem’s marginal cost function for manufacturing and selling polyglue is
MCL = 5,000 + 5QL
The aggregate marginal cost function for the other manufacturers of polyglue is
ΣMCF = 2,000 + 4QF
B. What is the total market demand for polyglue at the price established by Alchem in Part (a)? How much of total demand do the follower firms supply?
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