eco204_summer_2009_HW_5

# eco204_summer_2009_HW_5 - University of Toronto, Department...

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University of Toronto, Department of Economics, ECO 204 2008 2009 S. Ajaz Hussain ECO 204 Summer 2009 S. Ajaz Hussain HW 5 Please help improve the course by sending me an e mail about typos or suggestions for improvements Question 1 In this question you will examine the properties of the cost, average cost, average variable, average fixed and marginal cost functions for the short Cobb Douglas production function: Q = L α k β . Note that capital is fixed at a level k. (a) When does this production function exhibit constant returns to labor? (b) Derive the short demand for labor (c) Derive the short run total cost functions and examine the functional form when there are increasing, constant and decreasing returns. (d) Examine the functional form of the average fixed cost function. (e) Examine the functional form of the average variable cost function. (f) Examine the functional form of the average cost function. (g) Give a returns to scale explanation for the long run U shaped AC curve and contrast this with a returns explanation for the short run U shaped AC curve. Restrict the discussion to the Cobb Douglas production function. (h) Examine the functional form of the marginal cost function. In particular, when is the MC curve above the AVC curve? When is the MC curve coincidental with the AVC curve? When is the MC curve below the AVC curve? Hint: derive MC and express it terms of AVC. 1

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University of Toronto, Department of Economics, ECO 204 2008 2009 S. Ajaz Hussain Question 2 In the discussions on long run AC and learning by doing, we’ve seen that learning by doing lowers the cost per unit (AC) for all ouputs regardless of the returns to scale. Put another way, regardless of what the (long run) AC curve looks like, learning by doing lowers the AC curve. Assume a company uses the short technology augmented Cobb Douglas production function: Q = A L α k β . Note that capital is fixed at a level k and the parameter A represents technological progress. Show that technological progress will lower the AVC but not the AFC, and examine the impact
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## This note was uploaded on 05/02/2011 for the course ECO 204 taught by Professor Hussein during the Fall '08 term at University of Toronto- Toronto.

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eco204_summer_2009_HW_5 - University of Toronto, Department...

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