Chapter 11: Pricing with Market Power BB Ex. 11.1 You are an executive for Super Computer, Inc. (SC), which rents out super computers at a rate of P cents per second (=0,01 $/second). SC has two types...

Suppose that all iPod owners consider only two options for downloading music to their MP3 players: purchasing songs from iTunes or copying songs from friends. With these two options, suppose the...


Chapter 11: Pricing with Market Power BB Ex. 11.1 You are an executive for Super Computer, Inc. (SC), which rents out super computers at a rate of P cents per second (=0,01 $/second). SC has two types of potential customers of equal number : 10 businesses and 10 academic institutions. Each business customer has the demand function Q = 10 - P, where Q is in millions of seconds per month; each academic institution has the demand Q = 8 - P. The marginal cost to SC of additional computing is 2 cents per second, regardless of the volume. There are no fixed costs. a) What are price, output , profits and DWL if you can price discriminate? b) Suppose you were unable to keep the two types of customers separate. What price maximizes your profits? What are your profits? BB Ex. 11.2 Knoebels Amusement Park in Elysburg, Pennsylvania, charges an access fee, £, to enter its Crystal Pool. It also charges p per trip down the pool’s water slides. Suppose that 400 teenagers visit the park, each of whom has a demand function of q1 = 5-p, and that 400 seniors also visit, each of whom has a demand function of q2 = 4-p. Knoebels’ objective is to set £ and p so as to maximize its profit given that it has no cost. a) What are the optimal £ and p given that Knoebels must charge both groups the same price ? b) Will profit be higher or lower when Knoebels can charge different prices to each group ? Calculate and explain. BB Ex. 11.3 The block-pricing monopoly in the figure below faces a linear demand curve for each (identical) customer. The inverse demand curve is p = 90 –q. The monopoly has a constant marginal and average cost of m = $30. The firm uses declining-block prices to maximise its profit. This means that he is able to set three prices, depending on the quantity a consumer purchases. (See figure below, where p1 is the high price charged on the first Q1 units (first block), p2 is a lower price charged on the next Q2 – Q1 units, p3 is the lowest price charged on the Q3 – Q2 remaining units, and Q3 is the total number of units actually purchased.) Use calculus to determine the profit-maximizing prices and the corresponding quantities. BB Ex. 11.4 A theme parc notices a difference in the demand function of the visitors on week days and on weekends or holidays. · On a regular day the demand function for a visit to the theme parc is : q1 = 40000 – 500p · On weekends or holidays the demand function is : q2 = 60000 – 500p q1 and q2 are the number of visitors and p is the price for an entrance ticket. The costs are : TC = 500 000 + 5qi + 0.0005qi² Determine the optimal price and calculate the profit for a normal week (5 week days and 2 weekend days). BB Ex. 11.5 What if the same nonlinear price discriminating monopoly of BB Ex. 11.3 can only set two prices instead of three prices. Use calculus to determine the profit-maximizing prices and the corresponding quantities.