Assignment:
Part 1
1. Ajax Cleaning product is a medium sized firm operating in an industry dominated by one large firm-title King Ajax produces a multithreaded 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:
TC= 800,000-5,000Q + 100Q²
(A)Compute the marginal cost curve for Ajax
(B)Given Ajax pricing strategy. What is the marginal revenue function for Ajax
2. Unique Creations holds a monopoly position in the production and sale of mag-nometers. The cost function facing Unique is estimated to be
TC= 100,000+20Q
a.What is the marginal cost for Unique
b.If the price elasticity of demand for Unique is currently -1.5, what price should Unique charge
c.What is the marginal revenue at the price computed in part (b)
3. Wyandotte Chemical Company sells various chemical 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 operation research department has estimated that a 15 percent increase in output would not affect fixed costs but would reduce average variable costs by 60 cent 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 a 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 product. Demand for the products is given by the following liner demand function
P= 600 -Qc-Q?
Where Qc and Q? are the quantities sold by the respective firms and P is the selling price. Total cost functions for the two companies are
TCc= 25,000 + 100Qc
TC?= 20,000 + 125 Q?
Assume that the firms act independently as in the cournot model (i.e. each firm assumes that the other firms 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)
2.Assume that two companies (A and B) are duopolist who produces identical products. Determine for the products is given by the following liner demand function
P= 200 - Q?-Q?
Where Q? and Q? are the quantities sold by the respective firms and p is the selling price. Total cost functions for the two companies are
TC? = 1,500+35Q?+Q²?
TC?= 1,200 + 20Q? + 2Q²?
Assume that the firms act independently as in the Cournot model (i.e. each firm assumes that the other firms output will not change).
a.Determine Firms A, Firm B, and total industry profits at the equilibrium solution found in part (a)
5. Alchem (L) is the price leader in the polyglue market. All 10 other manufacture (follower [F] firms) sell polygue 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 polygue is given by the following function (Q?=Q?+ Q?)
P=20,000 - 4Q?
Alchem's marginal cost function for manufacturing and selling polygue is
MC?=5,000+5Q?
The aggregate marginal cost function for the other manufacture of polygue is
∑MC?=2,000 + 4Q?
a.To maximize profits, how much polygue should Alchem produce and what price should it charge?
b.What is the total market demand for polygue at the price established by Alchem in part (a)? How much of total demand dot he following firms supply?