Based on the following graph (which summarizes the demand, marginal revenue, and

Question

Based on the following graph (which summarizes the demand, marginal revenue, and relevant costs for your product), determine your firm’s optimal price, output, and the resulting profits for each of the following scenarios:

a. You charge the same unit price to all consumers.

Price: $

Output:  units

Profits: $  


b. You engage in first-degree price discrimination.

Price and output:

Charge the maximum price on the demand curve starting at $100 down to $40 for each infinitesimal unit up to 6 units.

Charge the maximum price on the demand curve starting at $100 down to $80 for each infinitesimal unit up to 2 units.

Charge the maximum price on the demand curve starting at $100 down to $60 for each infinitesimal unit up to 4 units.

Charge the maximum price on the demand curve starting at $100 down to $20 for each infinitesimal unit up to 8 units.

Profits: $  


c. You engage in two-part pricing.

Fixed fee: $

Per-unit fee: $

Output:  units

Profits: $  


d. You engage in block pricing.

Package size:  units

Package price: $

Profits: $

Price 110 1 100 90 80 70 60 50 40 30 20 10 MC = AC MR 0 1 2 3 45 6 7 8 9 10 11 12 13 14 15 Quantity

Explanation / Answer

(a) When charge the same unit price to all consumers : Then the condition for this is when MR= MC means marginal revenue is equal to marginal cost .

So, MR= MC is when Q=4 units and P=$ 60.

Profit = total revenue( =P * Q) - Total cost (AC * Q)

= (60 * 4) - (20 * 4) ( because AC = $20 given in the graph)

= $ (240 - 80) = $160

Therefore Price= $ 60

Quantity = 4 units.

Profits = $160.

(b) Engage in first degree price discrimination:

Price and output is different for different consumers . For Q=1 then price will be charged = 90.

For Q= 2 then price will be charged = 80 .

For Q= 3 , P= 70.

For Q=4 ,P= 60

For Q= 5, P= 50

For Q= 6,P=40

For Q=7, P=30

For Q=8 , P=20

Charge the maximum price on the demand curve starting at $100 down to $40 for each infinitesimal unit up to 6 units. Then profits = 6(100-40 ) (0.5) = 6 * 60 (0.5) = $180.

Charge the maximum price on the demand curve starting at $100 down to $80 for each infinitesimal unit up to 2 units. Then profits = 2(100-80)(0.5) = 2 * 20(0.5) = $20.

Charge the maximum price on the demand curve starting at $100 down to $60 for each infinitesimal unit upto 4 units . Then profits = 4(100-60)(0.5) = $80

Charge the maximum price on the demand curve starting at $100 down to $20 for each infinitesimal unit upto 8 units. Then profits = 8(100-20) (0.5) = $320.

(c) Engage in two -part pricing:

Charge a fixed fee of $320 and per unit fee of $20.Output is 8 units and total profits are $320.

Therefore, Fixed fee = $320

Per unit fee : $20 per unit

Output : 8 units

Profits: $320

(d) Engage in block pricing :

Create a package of 8 units and sell it for $480. Total profits at this will be $320.

Package price : $480

Package size : 8 units

Profits: $320.

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