Suppose the price of a filet mignon at Texas Roadhouse is $10

Economics Dec 23, 2020

Suppose the price of a filet mignon at Texas Roadhouse is $10. When Michael's old income was $2,000 per month, his old monthly demand for filets was Q = 15 - 0.25P. When Michael got a pay raise and began to earn a new income of $2,200 per month, his demand shifted outward to a new function of Q = 20 - 0.25P. Given this information, find Michael's income elasticity for filets.

Expert Solution

Income elasticity is the percentage change in quantity demanded divided by the percentage change in income. We first compute the percentage change in income:

(2200 - 2000) / 2000 = 10%

When price is 10, quantity demanded = 15 - 0.25 * 10 = 12.5. When income is 2200, quantity demanded = 20 - 0.25 * 10 = 17.5. The percentage change in quantity demanded = (17.5 - 12.5) / 12.5 = 40%.

So income elasticity = 40% / 10% = 4.

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