Wk 7 - Chapter 13 and Chapter 14 Problems

# Tr 1 p 1 q 1 60 2q 1 q 1 60q 1 2q 1 2 tr 2 p 2 q 2 40

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TR 1 = P 1 ∙Q 1 = (60-2Q 1 ) ∙Q 1 = 60Q 1 -2Q 1 2 TR 2 = P 2 ∙Q 2 = (40-Q 2 ) ∙Q 2 = 40Q 2 –Q 2 2 TC = 10 + 8Q 1 + 8 Q 2 π = TR - TC = - 10 + 52Q 1 - 2Q 1 2 + 32Q 2 - Q 2 2 b) What are the profit-maximizing price and outlet levels for the product in the two markets? Q 1 = 52 - 4Q 1 = 0 Q 1 * = 13 units P 1 * = 60 - 2(13) = \$34/unit. Q 2 = 32 - 2Q 2 = 0 Q 2 * = 16 units P 2 * = 40 - 16 = \$24/unit. c) At these levels of output, calculate the marginal revenue in each market. TR 1 = 60Q 1 - 2Q 1 2 MR 1 = 60 - 4Q 1 = 60 - 4(13) = \$8/unit. TR 2 = 40Q 2 - Q 2 2 MR 2 = 40 - 2Q 2 = 40 - 2(16) = \$8/unit.

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Myisha Coleman May 26, 2013 8. The Pear Computer Company just developed a totally revolutionary new personal computer. It estimates that it will take competitors at least two years to produce equivalent products. The demand function for the computer is estimated to be P = 2,500 – 0.0005Q The marginal (and average variable) cost of producing the computer is \$900. a) Compute the profit-maximizing price and output levels assuming Pear acts as a monopolist for its product. P = 2500 - .0005Q and MC = 900 and TR = P∙Q, so TR = 2500Q - .0005Q 2 MR = 2500 - .001Q = 900 at the most profitable output. Q* = 1,600,000 units, so P* = 2500 - .0005(1,600,000) = \$1700/unit b) Determine the total contribution to profits and fixed costs from the solution generated in Part (a). Profit contribution = 1700(1,600,000) - 900(1,600,000) = \$1,280,000,000 Pear Computer is considering an alternative pricing strategy of price skimming. It plans to set the following schedule of prices over the coming two years: Time Period Price Quantity Sold 1 \$2,400 200,000 2 2,200 200,000 3 2,000 200,000 4 1,800 200,000 5 1,700 200,000 6 1,600 200,000 7 1,500 200,000 8 1,400 200,000 9 1,300 200,000 10 1,200 200,000 c. Calculate the contribution to profit and overhead for each of the 10 time periods and prices.
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