Please teach not just solve with steps why income >price interior solutions A consumer has preferences over two goods represented by the utility function u(x₁, x2) =21+2√3₂.(a) Sketch this consumer's indifference curves.Solution: The indifference curves are conver, and are horizontal translations of eachother.(b) Find the Marshallian demand function z(p, w).Solution: The first-order conditions have a solution with x1, x2 ≥ 0 if w≥. Whenwe get a corner solution. Putting these together givesx(p, w) =if((-- -· (2) ²) iu≥ #1 (0, #)otherwise.Since preferences are conver, the solution to the first-order conditions is indeed a mazi-mum.EXPLAIN:Suppose that, initially, prices are p = (p₁, p2) and the consumer has wealth w satisfyingw>. If the price of good one doubles while, at the same time, the price of good twois cut in half, is the consumer made better or worse off (or is it impossible to determine)?and w>P2so the indirect utilities before and after the change are v = = + 2² and v² = ₁ + 2/2 =P2Solution: Let p₁ = 2p₁ and p2=2. Since w > SP² we have w >"W + respectively. Hence v > v if + 2 > 201 + 1, which is equivalent to2p1 P26p²w>P2by the change in prices.Find the expenditure function e(p, u) without solving the expenditure minimizationproblem.Since this last condition holds by assumption, the consumer is made worse off

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A consumer has preferences over two goods represented by the utility function (1₁,1₂)= 71 +2√72. (a) Sketch this consumer's indifference curves. Solution: The indifference curves are conver, and are horizontal translations of each other. (b) Find the Marshallian demand function z(p,w). Solution: The first-order conditions have a solution with 11,12 ≥ 0 if w ≥ . When w< we get a corner solution. Putting these together gives z(p. w) = {( ( 5 −2, (2) ²) if w ≥ Å 1 (0, =) otherwise. Since preferences are conver, the solution to the first-order conditions is indeed a mari- mum.

A consumer has preferences over two goods represented by the utility function (1₁,1₂)= 71 +2√72. (a) Sketch this consumer's indifference curves. Solution: The indifference curves are conver, and are horizontal translations of each other. (b) Find the Marshallian demand function z(p,w). Solution: The first-order conditions have a solution with 11,12 ≥ 0 if w ≥ . When w< we get a corner solution. Putting these together gives z(p. w) = {( ( 5 −2, (2) ²) if w ≥ Å 1 (0, =) otherwise. Since preferences are conver, the solution to the first-order conditions is indeed a mari- mum.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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