Jim Whitney Economics 250

Monday, April 01, 2013
 

Monopoly worksheet

Part 1: The math and geometry of profit maximization
 
1. You are a monopolist with the following demand and cost information:
        Q = 40 - 2P
        TC = 80 + 4Q (note: this cost equation => a natural monopoly)
a. What is the equation for your inverse demand function?
     
b. What is the equation for your marginal revenue (MR)?
     
c. What is the equation for your marginal cost (MC)?
 
d. Find your profit-maximizing output level (Qm), and calculate each of the following:
Qm= MR= MC=  
P= TR= TC= Profits =
 
e. What is the equation for your ATC?
 
f. Complete the following table of ATC values:
Q ATC
8 14
16  
24  
32  
 
g. In the diagram to the right, plot each of the following:
   (1) Demand, (2) MR, (3) MC, and (4) ATC.
h. Shade in your profits at your profit-maximizing output level.

 

 

Part 2: Elasticity, price and markup
 
2. a. What is the value of your elasticity of demand at your profit-maximizing output level?
     

 
b. Decide whether the following is true or false, and support your answer: A simple monopoly never operates in the region of inelastic demand.

 

 
c. Recall the formula: MR = ((|e|-1)/|e|)P. Prove the following: A profit-maximizing monopolist charges a price (P) = (|e|/(|e|-1))MC. [Note: (|e|/(|e|-1)) is called the monopolist's markup of price over marginal cost.]

 

 

 
d. Verify that you are following the monopoly markup pricing rule at your profit-maximizing output level.

 

 

 
  e. Suppose that a monopoly has a constant marginal cost = $1 and faces a constant-elasticity demand equation (Q = aPe; e has a negative sign). Complete the following table to show the price the monopoly would charge:
 
|e| Price
2  
3