Question

d. U (1, ) (1a)(b-a For the utility function above, find the consumer's optimal consumption bundle when prices of goods 1 and 2 are pl and p2, and the consumer has an income m 1. 2. For the utility function above, find the consumer's optimal consumption bundle when prices of goods 1 and 2 are pl and p2, and the consumer has an endowment (el, e2) of the two goods For each of your answers in question 2, write down the consumer net det demands for the two 3. goods at prices pl and p2. Find the ratio of pricesfor which the net demand for good 1 is p2 zero. Also find the price ratio at which the net demand of good 2 is zero.

Answer 1

Utility: u(x_1, x_2) = (x_1 + a)^alpha (x_2 + b)^1 - alpha prices of good 1 & 2 are p_1 delta p_2 respectively the income is m. Budget constraint: p_1 x_1 + p_2 x_2 = m equation (1) At the optimal: slope of Indifference = slope of budget line curve MR5 = -p_1/p_2 - mi_1/mu_2 = -p_1/p_2 d/dx_1 (x_1 + a)^alpha (x_2 + b)^1 - alpha/d/dx_2 (x_1 + a)^alpha (x_2 + b)^1 - alpha = p_1/p_2 alpha (x_1 + a)^alpha - 1 (x_2 + b)^1 - alpha/(1 - alpha (x_1 + a)^alpha (x_2 + b)^- alpha = p_1/p_2 alpha (x_2 + b)/(1 - alpha) (x_1 + a) = p_1/p_2 (x_2 + b) = (1 - alpha/alpha) (p_1/p_2) (x_1 + a) x_alpha = (1 - alpha/alpha) p_1/p_2 (x_1 + a) - b [x_2 = (1 - alpha) p_1 (x_1 + a) - alpha p_2 b/alpha squareroot 2] \r\n substituting value of x_2 in Budget constraint p_1 x_1 + p_2 ((1 - alpha) p_1 (x_1 + a) - alpha p_2 b/alpha p_2) =