eco204_HW_12 - University of Toronto Department of...

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Unformatted text preview: University of Toronto, Department of Economics, ECO 204 20082009 S. Ajaz Hussain ECO 204 20082009 Ajaz Hussain HW 12 Question 1 Suppose the Ontario government levies a fine on tobacco companies for misleading smokers about the dangers of smoking (a similar measure was passed in the US a few years ago). If the fine is collected as a lump sum tax, should tobacco companies raise the price of cigarettes to compensate for the fine? Question 2 In Lecture 14 we discussed the envelope theorem which gives us a simple technique for evaluating the change in the optimized objective when a parameter changes. In this question, you will reproduce some of the results in Lecture 14. Suppose a company using ECO 204 and ECO 220 tools estimates the demand and cost functions to be linear: P(Q) = a bQ C(Q) = TFC + c Q Where P is in $, Q is in `000s and a, b, TFC, c are positive parameters (a) Interpret the parameters a, b, TFC, c. (b) Assuming there is no opportunity cost and unlimited capacity, derive an expression for the firm's profits with Q as the decision variable. (c) What is the optimal Q expressed as a function of the parameters a, b, TFC and c? 1 University of Toronto, Department of Economics, ECO 204 20082009 S. Ajaz Hussain (d) Use the envelope theorem to gauge the impact on the optimized profits from an increase of 1 unit from each the parameters a, b, TFC and c, holding all other parameters constant. (That is, what is the impact of raising the parameter a by 1 unit holding all other parameters constant). (e) Interpret the results in part (d). (f) If you, the manager had a budget to change one of the parameters (for the same cost) which one parameter would you pick and what would you do? (g) Suppose you didn't know the envelope theorem. What is the impact on the optimized profits from an increase of 1 unit of the parameter a? (Of course, you should have the same answer as in part (d)). (h) Use the envelope theorem to gauge the impact on the optimized profits with price as the decision variable. Question 3 In Lecture 14 we discussed how if a monopolist could charge a lower price than competitive markets, provided the monopolist had a low enough MC (see transport example with railways vs. horses). Suppose all perfectly competitive companies have a constant MCc. Suppose also that the market has a linear market demand curve P(Q) = a bQ. Suppose the monopolist has a constant MCM. What must be true about MCM if the monopoly price (PM) is lower than the competitive price (PC). Hint: See Lecture 14. 2 ...
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