Question

3. Managers at C-Pal Industries, a monopolist, face 100 identical individuals, each with an inverse demand curve given by P = 10 - Q C-Pal has constant marginal cost of $4 and fixed costs of $500. A. Draw the diagram showing each consumer's individual demand curve and marginal cost (= AVC since MC is constant). What are profit-maximizing price and quantity per customer, as well as profits per customer, when C-Pal engages in uniform pricing with no other pricing strategies imposed? B. C. Now assume that C-Pal can engage in first-degree price discrimination. This means that it can charge each consumer its true willingness to pay for each unit purchased. Is C-Pal able to improve on the outcome under uniform pricing? Managers at C-Pal have decided to implement a two-part pricing strategy that charges a fixed fee to purchase any units at all, plus a price per unit. What fixed fee and price should it set? What are C-Pal's profits? Now C-Pal's marketing department has approached management with a plan to sell the good as a block, with consumers required to purchase the quantity that has been packaged together. What block price should be set? What are C-Pal's profits. E.

Answer 1

DEMAND FUNCTION Q = 10-P COST 200 DEMANDU CURVE -MC - AVC 3 . 6 8 10 o 4 Scanned with CamScanner B. Since all individuals have identical, the inverse demand function for 100 individuals can be written Q = 1000 - 100P Or P= 10 - .010 Total Revenue of the firm, R = PQ = 100-.0102 and total cost C = 500+ 4Q Profits n =R-C= 10Q -.0102 – 500 - 4Q The profits will be maximum when dot = 6-.02Q = 0 or Q=300 Thus, total quantity produced will be 300 and price will be $7. For Q = 300, total profit of the firm will be $400 and per person profit will be $4. C. If the firm can charge equal to an individual's willingness to pay, then the firm can charge $9 for the first 100 units, $8 for the second 100 units, $7 for the third 100 units, $6 for the fourth 100 units sold and so on. Since marginal cost of the firm is $4 for each unit produced. The firm will produce 600 unit at which price will be $4 and total revenue will be $400. Remember that unlike the previous situation, the prices of previous units sold will remain unchanged. Thus, marginal revenue of the firm will be equal to marginal cost at price $4 at which 600 units will be sold. The total revenue of the firm will be $3,900 for these 600 units. The cost of production for 600 units will be $2,900. Thus, the profit of the firm will be $1,000. Thus, the firm will earn higher profit ($600) compared to one fixed price. D. The firm will charge a fixed fee of $15 and fix $4 as the price of one unit purchased. In this way, the firm will be able to capture the entire surplus and earn a profit of $1,000. E. The firm should sell the goods as a block of 6 units and price the bundle at $39. In this case again the profit of firm will be $1,000.