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Answer Key Assignment #3 Questions from chapter 11: 1- Short run supply = MCi . We have MC i = 4 + Q i , and hence Q i = MC i 4. Q i = Q = MC i 4000, or Q = 1000 MC 4000. For profit maximization, MC = P, and so Q = 1000 P 4000, which means that industry supply is given by P = 4 + 0.001Q. Hence short run equilibrium Q occurs where 4 + 0.001Q = 10 0.002Q. With 0.003Q = 6, we have Q = 2000 units, and P = \$6/unit. 10 6 4 2000 S D Q P Consumer surplus Producer surplus Consumer surplus = area of upper triangle = (10 6)(2000)/2 = \$4000. Producer surplus = area of lower triangle = (6 4)(2000)/2 = \$2000. Total loss of surplus = \$6000. 2- a) With the new process, your costs, excluding your payment for use of the patent, will be TC' = 4 + Q + Q 2 . To find your profit maximizing output level, we equate your new marginal cost, MC' = 1 + 2Q, to the industry price, which, as before, will be the minimum value of the average cost curve associated with the prevailing technology: LAC = 8/Q + 2 + 2Q => dLAC/dQ = 2 8/Q 2 = 0 => Q* = 2 => LAC = 10 = P*. If we use Q' to denote the patent-holding firm's profit-maximizing output level, we have MC'=10 = 1 + 2Q'

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=> Q' = 4.5. The patent holder's economic profit will thus be TR TC = 45 [4 + 4.5 + (4.5) 2 ] = \$16.25. So the most you would be willing to pay for the patent is \$16.25. b) Because the patented process can reduce the costs of each of the 1001 firms by half, it is worth considerably more than \$16.25; hence the inventor would not be willing to sell exclusive rights to its use to one firm at that price. For example, he could sell the patent to two firms for about \$16.24 each, and so on. At some point, of course, attention would have to be given to the elasticity of market demand. For example, if all 1001 firms produced 4.5 units instead of 2 units, industry supply
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