Answer to Question #203084 in Math for Ishita

Question

Each week an individual consumes quantities x and y of two goods, and works for l hours. These three quantities are chosen to maximize the utility function

U(x, y, l) = α ln x + β ln y + (1 − α − β) ln (L − l)

which is defined for 0 ≤ l < Land for x,y > 0. Here α and β are positive parameters satisfying α +β < 1. The individual faces the budget constraint px + qy = wl, where w is the wage per hour. Find the individual’s demands x^∗, y^∗, and labour supply l^∗ as functions of p, q, and w.

Answer 1

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