(3e) Hello! I just want to ask for help whether the answers in the given pictures are correct. If it's not, please help me recheck and resolve it. Please refer to the given pictures below for the answers and questions. Make sure the formulas and solutions are right and clear. NOTE: Type only your answers. Please do not handwritten your answers. 2. Consider the utility function of individual A given by UA (X,Y) = X".5yd.5 in answering theitems below:a. Calculate the marginal utility for each good (MUx & MUY) of individual A and themarginal rate of substitution (MRSXY). Interpret your computed values.b. If Px 3D 0.5, PүMultiplier Method.1, and I = 10, solve for X*, Y*, and U* using the Lagrange Step 1Given Utility functionU=x0.5y0.5Px=0.5Ру-1|=10Step 2U - X0.5ү0.5dUMUX =dUMUYDYMUXMRS%3DMUYPart 1)Solving for the MRSU = X0.5 y0.5- (1)-(2)MUx =dU = – -= 0. 5X-0.5 y 0,5 = 0 -MUy == 0. 5X0.5 Y -0.5 = 0 – –%DdYВу еquation 1 and 20.5X-05y0.50.5x05y-0.5--0.:MRS =YMRS =XMarginal utility of X shows the additional utility received by 1 additional unitof X consumption.second order is negative, therefor it represents law of diminishing marginalutility.Marginal utility of Y shows the additional utility received by 1 additional unitof Y consumption.second order is negative, therefor it represents law of diminishing marginalutility.MRS represent sacrifice of Y inoredr to get 1 extra unit of XHere to get 1 extra X he is ready to forgone 1 Y.Part b)Budget constraint10 = 0. 5X + YBy lagrange functionMax U = X05y05 + 2(10 – – Y )М0.5X -ОМaxU0. 5X-0.5 y0.5 – 0. 51Xe= 0. 5X0.5 Y-0.5 – 1 = 0 – –(2(1) -ƏMaxUdYВу еquation 1 and 2* = 4Y0.5X1Y = 0. 5XBy substituting into budget constraint10 = 0. 5X + Y10 = 0. 5X + Y0. 5X10 = XBy plugging X into YY = 0. 5XY = 0. 5 * 10Y = 5X* = 10, Y * 5U =100.550.5U =7. 0708%DU* 3D 7 аррrox.

utility means the satisfaction consumer derives from the consumption . it is measured in terms of…

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.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.12P

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he Calculus of Utility Maximization and Expenditure Minimization -End of Appendix Problem uppose that there are two goods, X and Y. The price of X is $2 per unit, and the price of Y is $1 per unit. There are two onsumers, A and B. The utility functions for the consumers are UA(X,Y)= X05.05 UB(X,Y)= X0.8y0.2 Consumer A has an income of $100, and Consumer B has an income of $300. Using Lagrangians, solve for the optimal bundles of goods X and Y for both consumers A and B. a. The optimal bundle for consumer A is X = 25 and Y* = 50 - b. The optimal bundle for consumer B is X = 120 and Y* = 60
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Pls help with thsi question Consider an Individual who buys films (F) and books (B) with the following utility function:?(?, ?) = 5? + 2?This individual also has the following incomes (m) and prices (pF and pB):? = $50, ?f= $5, ?b= $10Given the above:1) Draw the utility functions for utility levels of 10 and 20. Draw these with films on the x-axis and books on the y-axis. 2) What is the MRS for these utility functions? Assume that films remain on the x-axis andbooks remain on the y-axis. 3) What is the consumption bundle that delivers the highest level of utility that is alsoaffordable?
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Assume that a person's vitility function is given Assume by the following function. TU = 2x¹¹2,¹/2 also that the price of x is 22 and the price of is 26 and that the budget is 2240. what is the optimal amount of goods x and that should be purchused with this budget? of y у
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