Part 1
1. Ajax Cleaning Products is a medium-sized firm operating in an industry dominated by one large firm Tile King. Ajax produces a multi-headed tunnel wall scrubber that is similar to a model produced by Tile King. Ajax decides to charge the same price as Tile King to avoid the possibility of a price war. The price charged by Tile King is $20,000.
Ajax has the following short-run cost curve:
,000 - 5,000Q + 100Q2.
A. Computer the marginal cost curve for Ajax.
B. Given Ajax's pricing strategy, what is the marginal revenue function for Ajax?
2. Unique Creations holds a monopoly position in the production and sale of manometers. The cost function facing Unique is estimated to be
TC = $100,000 + 20Q
A. What is the marginal cost for Unique?
C. What is the marginal revenue at the price computed in Part (b)?
3. Wyandotte Chemical Company sells various chemicals to the automobile industry. Wyandotte currently sells 30,000 gallons of polyol per year at an average price of $15 per gallon. Fixed costs of manufacturing polyol are $90,000 per year and total variable costs equal $180,000. The operations research department has estimated that a 15 percent increase in output would not affect fixed costs but would reduce average variable costs by 60 cents per gallon. The marketing department has estimated the arc elasticity of demand for polyol to be -2.0.
A. How much would Wyandotte have to reduce the price of polyol to achieve a 15 percent increase in the quantity sold?
B. Evaluate the impact of such price cut on (i) total revenue, (ii) total costs, and (iii) total profits.
Part 2
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:
- Qc- Qd
Where Qc and Qd are the quantities sold by the respective firms and P is the selling price. Total cost functions for the two companies are
,000 + 100Qc
,000 + 125Qd.
Assume that the firms act independently as in the Cournot model (i.e., each firm assumes that the other firm Â'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 the equilibrium output found in Part (a). This is answer for 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:
Â- Qa - Qb
Where Qa and Qb are the quantities sold by the respective firms and P is the selling price. Total cost functions for the two companies are:
,500 + 55Qa + Q^2a
,200 + 20Qb + 2Q^2b .
Assume that the firms act independently as in the Cournot model (i.e., each firm assumes that the other firm Â's output will not change).
B. Determine Firm A, Firm B, and total industry profits at equilibrium solution found in Part (a).
3. Alchem (L) is the price leader in the polyglue market. All 10 other manufacturers (follower [F] firms) sell polyglue at the same price as Alchem. Alchem allows the other firms to sell as much as they wish at the established price and supplies the remainder of the demand itself. Total demand for polyglue is given by the following function ( +QF):
,000 - 4 QT
Alchem marginal cost function for the manufacturing and selling polyglue is
,000 + 5QL
The aggregate marginal cost function for the other manufacturers of polyglue is
?,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?