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

Quizplus · Accepted Answer

To extract all consumer surplus from daytime buyers, the firm needs to set the access charge equal to the maximum amount the daytime buyers are willing to pay for the product. From the demand function, we can see that the maximum amount they are willing to pay is $8 per unit. Therefore, the optimal access charge is:

A* = 50 x $8 = $400

To determine the optimal usage fee, we need to set the usage fee at a level that maximizes the firm's profit. The profit function is given by:

π = (p - AVC)q - FC - A

Substituting the demand function and simplifying, we get:

π = ($8 - $12)q - $250,000 - A
π = -$4q - $250,000 - A

To maximize the profit, we need to set the derivative of the profit function with respect to q equal to zero:

dπ/dq = -4 = 0

Therefore, q = 0.

This implies that the firm should not charge any usage fee at all, as it will maximize its profit by giving the product away for free.

Hence, the optimal two-part pricing plan for extracting all consumer surplus from the daytime buyers is:

Access charge = $400 
Usage fee = $0

The answer is C.

A Firm Sells Its Product to Two Groups of Buyers