2.99 See Answer

Question:


(Instructor-provided spreadsheet recommended) Consider an individual’s utility function over two goods, qm and qs, where m indicates the primary market in which a policy will have its effect and s is a related secondary market:

Where α, βm, βs, and γ are parameters such that βm> 0, and βs> 0, βm< (1-γqs)/2qm, βs < (1-γqm)/2qs, and γ < pmβs/ps + psβm/pm. For purposes of this exercise, assume that α =1, βm = 0.01, βs = 0.01, and γ = -0.015. Also assume that the person has a budget of $30,000 and the price of qm, pm, is $100 and the price of qs, ps, is $100. Imagine that the policy under consideration would reduce pm to $90.
The provided spreadsheet has two models. Model 1 assumes that the price in the secondary market does not change in response to a price change in the primary market. That is, ps equals $100 both before and after the reduction in pm. Step 1 solves for the quantities that maximize utility under the initial pm. Step 2 solves for the quantities that maximize utility under the new pm. Step 3 requires you to make guesses of the new budget level that would return the person to her original level of utility prior to the price reduction — keep guessing until you find the correct budget. (You may wish to use the Tools|Goal Seek function on the spreadsheet instead of iterative guessing.) Step 4 calculates the compensating variation as the difference between the original budget and the new budget. Step 5 calculates the change in the consumer surplus in the primary market.
Model 2 assumes that ps = a + b qs. Assume that b=0.25 and a is set so that at the quantity demanded in Step 2 of model 1, ps=100. As there is no analytical solution for the quantities before the price change, Step 1 requires you to make guesses of the marginal utility of money until you find the one that satisfies the budget constraint for the initial pm. Step 2 repeats this process for the new value of pm. Step 3 requires you to guess both a new budget to return the person to the initial level of utility and a marginal utility of money that satisfies the new budget constraint. A block explains how to use Tools|Goal Seek to find the marginal utility consistent with your guess of the new budget needed to return utility to its original level. Step 4 calculates the compensating variation. Step 5 calculates the change in the consumer surplus in the primary market and bounds on the change in consumer surplus in the secondary market.
Use these models to investigate how well the change in social surplus in the primary market approximates compensating variation. Note that as utility depends on consumption of only these two goods, there are substantial income effects. That is, a price reduction in either of the goods substantially increases the individual’s real income. Getting started: The values in the spreadsheet are set up for a reduction in pm from $100 to $95. Begin by changing the new primary market price to $90 and resolving the models.



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2.99

See Answer