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

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To maximize profit, the firm should set a two-part pricing plan where the daytime buyers pay an access charge and a usage fee. Since the firm wants to extract all consumer surplus from the daytime buyers, the access charge should be equal to the maximum amount the buyers are willing to pay, which is their consumer surplus. Using the formula for consumer surplus (CS = 1/2(Q-MB)), where Q is the quantity bought, and MB is the marginal benefit (or price) the buyers are willing to pay, we find that the maximum consumer surplus for the daytime buyers is: CS = 1/2(50-15)($100) = $1,875 So, the optimal access charge is $1,875. To find the optimal usage fee, we need to calculate the quantity that the daytime buyers will purchase at the optimal access charge. Since the demand function is given as D_D, we know that at a price of $100 (i.e. the access charge), the quantity demanded is 15. Therefore, the total revenue from the access charge is: TR = Q x A = 15 x $1,875 = $28,125 The profit-maximizing usage fee is the one that sets marginal revenue equal to marginal cost. The marginal revenue from each unit sold is the usage fee minus the variable cost (MC = SMC = AVC = $12). Since there are 50 daytime buyers and each buys 15 units, the total quantity sold is 750 units. Therefore, the profit-maximizing usage fee is: MR = MC P - AVC = 0 P = AVC = $12 Since the buyers are willing to pay up to $100 for each unit, the profit-maximizing usage fee is: $100 - $12 = $88 So, the optimal two-part pricing plan for the daytime buyers is an access charge of $1,875 and a usage fee of $88 per unit. The total profit for the firm is: Profit = TR - TC = ($28,125 + 50 x $88 x 15) - $250,000 = $25,625.

A Firm Sells Its Product to Two Groups of Buyers