In Questions a firm sells its product to two groups of buyers: daytime buyers and nighttime buyers. There are 50 daytime buyers, all of whom have identical demands given by D D in the figure below. There are 50 nighttime buyers, all of whom have identical demands given by D N in the figure below. The firm's variable costs are constant (SMC = AVC = $12) and its total fixed cost is $250,000. The marketing director must devise a two-part pricing plan that will maximize the firm's profit.
-Suppose the marketing director ignores the nighttime market and wishes to extract all consumer surplus from the daytime buyers. The optimal access charge is $_________ and the optimal usage fee is $______ per unit.
A) A* = $1,000 and f * = $12
B) A* = $2,400 and f * = $12
C) A* = $7,744 and f * = $12
D) A* = $9,856 and f * = $12

Question

In Questions  a firm sells its product to two groups of buyers: daytime buyers and nighttime buyers. There are 50 daytime buyers, all of whom have identical demands given by D D in the figure below. There are 50 nighttime buyers, all of whom have identical demands given by D N in the figure below. The firm's variable costs are constant (SMC = AVC = $12) and its total fixed cost is $250,000. The marketing director must devise a two-part pricing plan that will maximize the firm's profit. 
-Suppose the marketing director ignores the nighttime market and wishes to extract all consumer surplus from the daytime buyers. The optimal access charge is $_________ and the optimal usage fee is $______ per unit.
A) A* = $1,000 and f * = $12 
B) A* = $2,400 and f * = $12 
C) A* = $7,744 and f * = $12 
D) A* = $9,856 and f * = $12

Quizplus · Accepted Answer

To extract all consumer surplus from daytime buyers, the firm must set its price equal to each buyer's willingness to pay. From the demand equation DS1U1B1DS1U1B0, we see that the daytime buyers' aggregate willingness to pay is:

50(100 - 2DS1U1B0) = 5000 - 100DS1U1B0

Thus, the optimal usage fee (f*) is $12 (the constant variable cost) and the optimal access charge (A*) is the amount that solves the following problem:

max (5000 - 100DS1U1B0 - A*)DS1U1B0 - 12DS1U1B0 - 250000

Taking the derivative with respect to DS1U1B0 and setting it equal to zero gives:

5000 - 200DS1U1B0 - A* - 12 = 0

Thus, A* = $7,744.

In Questions a Firm Sells Its Product to Two