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eco204_summer_2009_practice_problem_14

# eco204_summer_2009_practice_problem_14 - University of...

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Unformatted text preview: University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain ECO 204 Summer 2009 S. Ajaz Hussain Practice Problems 14 Please help improve the course by sending me an email about typos or suggestions for improvements Note: Please don't memorize these solutions in the expectation that similar questions will appear on tests and exams. Instead, try to understand how to derive the answer as you'll be tested on techniques and applications, not on memorization. Moreover, tests and exams will cover topics and techniques that may not be in these practice problems. You are urged to go over all lectures, class notes and HWs thoroughly. Question 1 In this question, you will examine a company with a Ushaped MC curve. Given that a perfectly competitive firm (a price taker) has a flat demand curve and therefore a MR curve that is also flat (and equal to the demand curve), there will be two points where MR = MC. You will practice and confirm that only one of these points maximizes profits and is an "equilibrium". This way you will see why ECO 100 only worked with the "right" side of a Ushaped MC curve. Suppose a perfectly competitive firm has the cost function: C = 25 log q + 0.5q2 Here the log is a "natural log" (to the base e). (a) Derive the MC and interpret it. Is it Ushaped? (b) Suppose the market price is \$15. Calculate the output or outputs where MR = MC. If you need to use it, here is the quadratic formula: for ax2 + bx + c = 0, x = [b +/ square root of (b2 4ac)]/2a. (c) We have seen that the smaller quantity where MR = MC cannot be an equilibrium and in fact does not maximize profits, whereas the larger quantity where MR = MC is an equilibrium and in fact maximizes profits. Prove this. 1 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain Question 2 The table below shows the MC of major producers of Copper. From this, one can graph the global supply curve of copper: (a) Suppose Russia is a "rational" Copper producer. Will it supply copper if the price of copper is 0.8? What if the price was 0.4? 2 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain (b) Suppose Russia is an "irrational" Copper producer. How much copper will it supply if the price of copper is 0.8? What if the price was 0.4? 3 ...
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