LINEAR PRICING: MONOPOLY

Reference:

C& P, Ch 3, p69-73, Ch 4, p88-107.

Frank, Jennings, and Bernanke,  pp. 258-74

This lecture we consider the choice of price by firms which must use linear pricing.

We also review some fundamental concepts of welfare economics which will allow us to assess the economic efficiency of various pricing mechanisms.

Linear Pricing

Under linear pricing all customers pay the same price per unit for all units purchased.

That is, there is such a thing as a single price ($/unit) for the good.

We shall see linear pricing is likely to occur in the following circumstances:

  1. Where it is costless for customers to trade the goods amongst themselves (costless arbitrage)
  1. Where consumers purchase at most 1 unit, and the firm cannot identify individual customer’s willingness to pay.

Monopoly

Market supplied by a single firm.

  • this firm will have ‘market power’ i.e. is a price setter.
  • Monopolist faces market demand curve:

Linear pricing with discrete demand

The firm sets a linear price, P. Note consumers will purchase the good if their MB³P.

  • assume if customers indifferent they purchase the good.
  • Recall that this means the MB is the firm’s demand curve.

Hence, in our example from lecture 2 the firm:

    Sales

(Movies a month)

Price 

($ per unit)

  Elle Joy  

Market

 
30.00   1 0 1  
25.00   1 1 2  
20.00   2 1 3  
15.00   2 2 4  
10.00   3 2 5  
5.00   3 3 6  
2.00   4 3 7  
0.00   4 3 7  

 

 

or:

 

         
Market Sales

(Movies a month)

  Price

($ per unit)

    Revenue
1   30.00     30
2   25.00     50
3   20.00     60
4   15.00     60
5   10.00     50
6   5.00     30
7   2.00     14

Suppose MC = 3, and fixed cost is 5

TC = 5 + 3Q

Market Sales

(Movies a month)

  Price 

($ per unit)

Revenue   Cost Profit  
1   30.00 30   8 22  
2   25.00 50   11 39  
3   20.00 60   14 46  
4   15.00 60   17 43  
5   10.00 50   20 30  
6   5.00 30   23 7  
7   2.00 14   26 -12  

The firm maximises profit by choosing to set price 20 with an output of 3.

Alternatively:

Market Sales

(Movies a month)

Price 

($ per unit)

Marginal

Revenue

Marginal

Cost

Marginal

Profit

1 30.00 30 3 27
2 25.00 20 3 17
3 20.00 10 3 7
4 15.00 0 3 -3
5 10.00 -10 3 -13
6 5.00 -20 3 -23
7 2.00 -21 3 -24

Max profit by producing all units which increase profit.

That is produce all units for which MR>MC.
Our example from lecture 2

  Marginal Benefit

($ per unit)

Quantity

(Movies a month)

  Elle Joy  
1   3.00 2.50  
2   2.00 1.50  
3   1.00 0.50  
4   0.20 0.00  
5   0.00 0.00  

Complete the following tables:

         
Market Sales

(Movies a month)

  Price

($ per unit)

    Revenue
1          
2          
3          
4          
5          
6          
7          

Suppose MC = 0, and fixed cost is 1, hence

TC = Q

Market Sales

(Movies a month)

Price 

($ per unit)

Marginal

Revenue

Marginal

Cost

Marginal

Profit

1        
2        
3        
4        
5        
6        
7        

Consumer surplus

Suppose Elle could buy movie ticket for $20 per ticket. The she would receive a net benefit for the first movie she saw of $30 – 20 = $10, for the second movie of $20 –20 = $0, (Note she would not see a 3rd movie because her net benefit for that movie would be $10-20 = -$10.)

Elle’s net benefit or “consumer surplus” for seeing 2 movies would be $10+0 = $10……………

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