HW6-solution - Econ 501 Homework Assignment 6 Due Tuesday...

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Econ 501 Homework Assignment 6 Due Tuesday Feb. 26th 1. BB 8.7 From the total cost curve, we can derive the average cost curve, 2 10 40 ) ( Q Q Q AC + = . The minimum point of the AC curve will be the point at which it intersects the marginal cost curve, i.e. 2 2 3 20 40 10 40 Q Q Q Q + = + . This implies that AC is minimized when Q = 5. By definition, there are economies of scale when the AC curve is decreasing (i.e. Q < 5) and diseconomies when it is rising ( Q > 5). 2. BB 8.9 a) Cost-minimizing quantities of inputs are equal to // LQ w r = and KQ r w = . Hence, in the long-run the total cost of producing Q units of output is equal to TC ( Q ) = 2 Qrw . For w = 1 and r = 1 we have TC ( Q ) = 2 Q . b) When capital is fixed at a quantity of 5 units (i.e., K * = 5) we have Q = K * L = 5 L . Hence, in the short-run the total cost of producing Q units of output is equal to S TC ( Q ) = 5 + Q /5. c) When w = 1 and r = 4 we have TC ( Q ) = 4 Q and S TC ( Q ) = 20 + Q /5. TC Q 25 5 STC ( Q ) TC ( Q )
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d) When w = 4 and r = 1 we have TC ( Q ) = 4 Q and S TC ( Q ) = 4 Q /5.
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HW6-solution - Econ 501 Homework Assignment 6 Due Tuesday...

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