Suppose you are the manager for a firm that has a monopoly on the product you pr

Question

Suppose you are the manager for a firm that has a monopoly on the product you produce and sell. Market research has shown that the demand by a typical customer for the product you sell is given by:

P=$180-3Q

Assume you have no fixed costs. From your production department, you are told that the variable costs of production are given by:

VC(Q)=0.75Q^2

a.   If you decide to offer the product for sale to all buyers at a single price, what price will you charge and how much will you sell to a typical customer?

b.   What profits per consumer will the firm earn under this pricing strategy?

c.   Now suppose you decide to use a simple block pricing strategy whereby you offer your product as a single package of a predetermined number of units. How much will you sell to a typical customer? (Hint: What is the optimal bundle size?)

d.   What price per consumer will the firm charge under this pricing strategy?

e.   Compare the profits under the two pricing strategies. Comment on the comparison.

Explanation / Answer

a) P = 180-3Q

R = 180Q-3Q^2

MR = 180-6Q

C = 0.75Q^2

MC = 1.5Q

Now MR=MC so

1.5Q=180-6Q

Q = 24

P = 180-3Q = 108

b) Profit = Revenue - cost = 108 - 0.75*24 = 90 per customer

c) Suppose Block quantity is Q1 and And Second block is Q2

P1 = 180-3Q1 Revenue1 = 180Q1-3Q1^2

P2 = 180-3Q2 Revenue1 = (180-3Q2)(Q2-Q1) = 180Q2-180Q1-3Q2^2+3Q1Q2

Profit = R1+R2 - TC where TC= 0.75Q2^2

Profit = -3Q1^2 + 180Q2 -3.75Q2^2+3Q1Q2

dPr/dQ1 = -6Q1+3Q2 = 0 so Q2=2Q1

dPr/dQ2 = 180-7.5Q2+3Q1 = 0 so Q1=10 And Q2=20

d. P = 180-3*10 = 150

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