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2. Consider the utility function of individual A given by Ua (X,Y) = X".5ya.s in answering the %3D items below: a. Calculate the marginal utility for each good (MUx & MUY) of individual A and the marginal rate of substitution (MRSXY). Interpret your computed values. b. If Px 0.5, Py = 1, and I = 10, solve for X*, Y*, and U* using the Lagrange %3D Multiplier Method.

2. Consider the utility function of individual A given by Ua (X,Y) = X".5ya.s in answering the %3D items below: a. Calculate the marginal utility for each good (MUx & MUY) of individual A and the marginal rate of substitution (MRSXY). Interpret your computed values. b. If Px 0.5, Py = 1, and I = 10, solve for X*, Y*, and U* using the Lagrange %3D Multiplier Method.

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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2. Consider the utility function of individual A given by UA (X,Y) = X".5yd.5 in answering the items below: a. Calculate the marginal utility for each good (MUx & MUY) of individual A and the marginal rate of substitution (MRSXY). Interpret your computed values. b. If Px 3D 0.5, Pү Multiplier Method. 1, and I = 10, solve for X*, Y*, and U* using the Lagrange
Transcribed Image Text:2. Consider the utility function of individual A given by UA (X,Y) = X".5yd.5 in answering the items below: a. Calculate the marginal utility for each good (MUx & MUY) of individual A and the marginal rate of substitution (MRSXY). Interpret your computed values. b. If Px 3D 0.5, Pү Multiplier Method. 1, and I = 10, solve for X*, Y*, and U* using the Lagrange
Step 1 Given Utility function U=x0.5y0.5 Px=0.5 Ру-1 |=10 Step 2 U - X0.5ү0.5 dU MUX = dU MUY DY MUX MRS %3D MUY Part 1) Solving for the MRS U = X0.5 y0.5 - (1) -(2) MUx = dU = – - = 0. 5X-0.5 y 0,5 = 0 - MUy = = 0. 5X0.5 Y -0.5 = 0 – – %D dY Ву еquation 1 and 2 0.5X-05y0.5 0.5x05y-0.5 --0.: MRS = Y MRS = X Marginal utility of X shows the additional utility received by 1 additional unit of X consumption. second order is negative, therefor it represents law of diminishing marginal utility. Marginal utility of Y shows the additional utility received by 1 additional unit of Y consumption. second order is negative, therefor it represents law of diminishing marginal utility. MRS represent sacrifice of Y inoredr to get 1 extra unit of X Here to get 1 extra X he is ready to forgone 1 Y. Part b) Budget constraint 10 = 0. 5X + Y By lagrange function Max U = X05y05 + 2(10 – – Y ) М 0.5X - ОМaxU 0. 5X-0.5 y0.5 – 0. 51 Xe = 0. 5X0.5 Y-0.5 – 1 = 0 – –(2 (1) - ƏMaxU dY Ву еquation 1 and 2 * = 4 Y 0.5 X 1 Y = 0. 5X By substituting into budget constraint 10 = 0. 5X + Y 10 = 0. 5X + Y0. 5X 10 = X By plugging X into Y Y = 0. 5X Y = 0. 5 * 10 Y = 5 X* = 10, Y * 5 U = 100.550.5 U = 7. 0708 %D U* 3D 7 аррrox.
Transcribed Image Text:Step 1 Given Utility function U=x0.5y0.5 Px=0.5 Ру-1 |=10 Step 2 U - X0.5ү0.5 dU MUX = dU MUY DY MUX MRS %3D MUY Part 1) Solving for the MRS U = X0.5 y0.5 - (1) -(2) MUx = dU = – - = 0. 5X-0.5 y 0,5 = 0 - MUy = = 0. 5X0.5 Y -0.5 = 0 – – %D dY Ву еquation 1 and 2 0.5X-05y0.5 0.5x05y-0.5 --0.: MRS = Y MRS = X Marginal utility of X shows the additional utility received by 1 additional unit of X consumption. second order is negative, therefor it represents law of diminishing marginal utility. Marginal utility of Y shows the additional utility received by 1 additional unit of Y consumption. second order is negative, therefor it represents law of diminishing marginal utility. MRS represent sacrifice of Y inoredr to get 1 extra unit of X Here to get 1 extra X he is ready to forgone 1 Y. Part b) Budget constraint 10 = 0. 5X + Y By lagrange function Max U = X05y05 + 2(10 – – Y ) М 0.5X - ОМaxU 0. 5X-0.5 y0.5 – 0. 51 Xe = 0. 5X0.5 Y-0.5 – 1 = 0 – –(2 (1) - ƏMaxU dY Ву еquation 1 and 2 * = 4 Y 0.5 X 1 Y = 0. 5X By substituting into budget constraint 10 = 0. 5X + Y 10 = 0. 5X + Y0. 5X 10 = X By plugging X into Y Y = 0. 5X Y = 0. 5 * 10 Y = 5 X* = 10, Y * 5 U = 100.550.5 U = 7. 0708 %D U* 3D 7 аррrox.
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