Question

Suppose a typical consumer's inverse demand function for bottled water at a resort area where one firm owns all the rights to a local spring is given by P = 15 - 3Q. The marginal cost for gathering and bottling the water is $3 per gallon. Determine the optimal price and output for each of the following scenarios.

You are a single price per unit monopolist.

You engage in first-degree price discrimination.

You engage in two-part pricing.

You engage in block pricing.

Why does a monopolist engage in pricing strategies beyond the single price model?

Answer 1

1)

Monopolist Equilibrium:

MR = MC'

P = 15 - 3Q

TR = P*Q

= (15 - 3Q)Q

= 15Q - 3Q^2

On differentiating

MR = 15 - 6Q

MR= MC

15 - 6Q = 3

-6Q = -12

Q = 2

P = 15 - 3(2)

= 15 - 6

= $ 9

Equilibrium Q =2

and P = $ 9

2)

First Degree Price discrimination:

P = MC

15-3Q = 3

3Q = 12

Q =4

P =3

Producer Surplus = 0.5 (15 -3)(4)

= 0.5 (12)(4)

= 0.5(48)

= 24

3)

Two part Pricing:

P = MC

15-3Q = 3

3Q = 12

Q =4

P =3

Consumer Surplus (CS) = 0.5 (12)(4)

= 24

Membership fee shall be $ 24

4)

Block Pricing is also called second degree price discrimination. Here, each block is priced differently.

(Question does not speak about number of blocks)

5)

Monopolist engage in pricing strategies beyond the single price model, to earn maximum profits.