A monopolist faces a market demand curve given by: Q_D = 70 - P. (a) If the mono

Question

A monopolist faces a market demand curve given by: Q_D = 70 - P. (a) If the monolist can produce at constant average and marginal costs of AC = MC = 6, what output level will the monopolist choose in order to maximize profits? What is the price at this level? What are the monopolist's profits? (b) Assume instead that the mono[>olist has a cost structure where total costs are described by: C(Q) =.25Q^2 - 5Q + 300. With the monopolist facing the same market demand and marginal revenue, what price-quantity combination will be chosen now to maximize profits? What will profits be? (c) Suppose instead that costs are given by: C(Q) =.0133Q^3 - 5Q + 250. Again, calculate the monopolist's optimal price-quantity combination. What will profit be? (d) Graph the market demand curve, the marginal revenue curve, and each of the three cost curves from parts (b)-(d). Notice that the monopolist's profit-making ability is constrained by the market demand curve (along with its associated MR curve) and the cost structure underlying production.

Explanation / Answer

Firm output Profit= (70-q)q- 6 q maximized at MR=MC

MR= 70- 2Q= 6=MC

Q= 32

P= 38

Profit= $1024

b) MC=.5Q-5

5= MC

Q= 30

P= 40

Profit= 825

c) .133q^3- 5 q+ 250

MC= .399Q^2- 5

MC= 5=.399q2-5= 10= .399q2 or

Q= 25

P=70-25=45

Profit=45*.133(25)^3-5(25)+250

45*2078-125+250

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