Show all calculations and state all assumptions

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Unformatted text preview: 204, S. Ajaz Hussain. Do not distribute. ❸ Evaluate at the optimal solution: Notice that because that: [⏟ Therefore, in step ❸ above: By the “value function” approach to get ❶ Express the objective function, the utility function, in terms of parameters: ❷ Substitute the optimal solutions: This is the same answer as the envelope theorem. (d) All else equal, what is the impact on the demand functions for goods 1 and 2 and the optimal utility due to a successful advertising campaign for good 2? Show all calculations and state all assumptions. 21 ECO 204 Chapter 3: Practice Problems & Solutions for Utility Maximization in ECO 204 (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Answer How does a persuasive advertising campaign for good 2 affect preferences? Intuitively, at any bundle, if the consumer has another unit of good 1 then in order to have the same level utility the consumer will now substitute a smaller amount of good 2 in exchange for another unit of good 1. That is, a greater affinity for good 2 leads to a smaller (in absolute terms). Now, the is: | when either Notice that | or . Let’s suppose while demand for good 2 rises. In this case, we see that: . Intuitively we know that demand for good 1 decreases ⏟ This means that with a greater affinity for good 2, the demand for good 1 goes down. Now: ⏟ ⏟ Since the denominator is larger than the numerator it means that as then . (3.10) Consider a consumer who has monotone preferences and perceives goods 1 and 2 as “perfect substitutes”. { } Assume all pecuniary parameters are strictly positive and that the consumption set is (a) Without solving the UMP, state and graph the various possible optimal choice “cases”. Answer From the linear utility model --- where the consumer perceives two good goods as perfect substitutes – given there are 3 possible outcomes (depending on preferences): 22 ECO 204 Chapter 3: Practice Problems & Solutions for Utility Maximization in ECO 204 (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. “Case B” “Case D” “Case C” C ( ) ( D ) ( ) B Case B occurs when | | ; Case C occurs when | | and Case D occurs when | | . (b) In general, which of the following two excise tax scheme will have a larger impact on the consumer’s optimal utility: a $0.01 quantity tax on good 1 versus a $0.01 quantity tax on good 2? Show all calculations and state all assumptions. Hint: Don’t forget there can be various possible optimal choices. Answer An excise tax raises the price of a good. We wanction defined over the consumption set { }: (a) Does this consumer have monotone preferences? Show all calculations. Answer Let’s compute the marginal utilities: Thus, good 1 is a “bad” good. Thus, good 2 is a “good” good. The consumer does not perceive both goods as “good” goods and does not...
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