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:
U = qm + αqs – (βmq2m + γqm qs + βsq2s)
where α, βm, βs, and γ are parameters such that βm>0, and βs>0, βm<(1-γqs)/2qm, βs<(1-γqm)/2qs, and γThe 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.