Question 4. Consider the following graph of an industry with a single producer (

Question

Question 4. Consider the following graph of an industry with a single producer (a monopolist). 4A. Derive the (algebraic) expression for the demand curve in the above picture. Show your work. 4B. Derive the firms marginal revenue curve. Show your work. (Hint: The firms marginal revenue curve is the dotted line that intersects the quantity axis at Q = 30). 4C. Derive the firms marginal cost curve. Show your work. 4D. That is the profit maximizing price and quantity that this monopolist will choose, assuming it cannot price discriminate (i.e., it is a single price monopolist)? Show your work. (Hint: For profit maximization, we want: MR = MC). Unlike in the case with perfect competition. however, here P MR). PRICE: _____ QUANTITY: _____

Explanation / Answer

A. Expression for demand curve

Q= 60-0.5P

B. Revenue =P*Q

Revenue = (120-2Q)*Q= 120Q-2Q^2

Marginal revenue = d(revenue)/dQ= 120-4Q

Marginal revenue = 120-4Q

C Let the equaltion of MC is

MC= mQ

It passes through (30,60)

60= m*30

M=2

MC curve equation is

MC= 2Q

D. For profit maximization, MR=Mc

120-4Q= 2Q

Q= 20

Price= 120-2*20= 80

Price= 80

Quantity = 20

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