An individual values two goods, X and Y, according to the following utility function: -1.33 U (X,Y) = 9 (0.33 X−0.75 +0.67 Y−0.75) The price of X is Px=2, and the price of Y is Py=3. The individual has 13 dollars. What is the Lagrangean for this problem? Please substitute the given values for variables where applicable. L= 9(0.33*X^(-0.75)+0.6*Y^(-0.75) +[13-2*X-3*Y BSD What are the first order conditions? Type L for X. ƏL ах ƏL ΟΥ ƏL Əx : Number Y= Number Number Number How much X and Y should this individual buy? (Round answers to the nearest two decimals. For example, 1.666 rounds to 1.67.) X= Number

An individual values two goods, X and Y, according to the following utility function: -1.33 U (X,Y) = 9 (0.33 X−0.75 +0.67 Y−0.75) The price of X is Px=2, and the price of Y is Py=3. The individual has 13 dollars. What is the Lagrangean for this problem? Please substitute the given values for variables where applicable. L= 9(0.33X^(-0.75)+0.6Y^(-0.75) +[13-2X-3Y BSD What are the first order conditions? Type L for X. ƏL ах ƏL ΟΥ ƏL Əx : Number Y= Number Number Number How much X and Y should this individual buy? (Round answers to the nearest two decimals. For example, 1.666 rounds to 1.67.) X= Number

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Suppose we are able to model the total utility function for the consumption of two goods, good x and good z. The utility function is structured as U(x, z) = 3x2 + z2 - 2xz. The consumer is faced with the prices of goods x and z. The price for each unit of good x and z is $1 each. The consumer has an income $1 (in thousands). How many units of each good should the consumer consume so as to maximize his/her utility?
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Tony is throwing a party at his Fraternity and is trying to choose what booze to buy. A bottle of vodka has three times the alcohol as a six-pack of beer. Assume that Tony only cares about the total amount of alcohol in his basket. (use vodka on the X-axis and beer measured in six-pack on the Y-axis) a) Devise a utility function to represent these preferences. b) Suppose a bottle of vodka costs $40, a six-pack of beer costs $10, and the budget is $200. Write the budget constraint. c) Solve Tony’s utility maximization problem and find the optimal combination. d) Suppose that a bottle of vodka cost has increased to $50. What will be his new optimal combination.
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While visiting family in Mexico, your professor has a budget of $ 255 ($ = pesos) that he spends on tacos and tequila. The price of tacos is $ 6 and a shot of tequila is priced at $ 16. During his visit the price of tacos changes to $ 5. Assume your professor has a Cobb-Douglas utility function with (tacos) parameter a = ( 27 / 100). How many shots of tequila does your professor purchase ? (Assume both goods are commodities.) (Answer is : 11.63)
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Utility maximization with a budget constraint. A hypothetical consumer spends all tgheir income on ramen noodles (N) and wild rice (W). N is the quantity of noodles; W is the quantity of wild rice. Their income is $1,600 per month. the price of noodles is $2 per package and the price of wild rice is $20 per pound. The utility function is U=sqrt(N*W). the MRS = -N/W. The budget constraint is: 1,600 = 2*N + 20*W Graph Qty of noodles (N) on vertical axis and Qty of wild rice (W) on horizontal axis. SOLVE: a. Graph the budget constraint. label all points. What is the slope of the budget constraint? b. Find the optimal quantities of noodles(# of packages) and the wild rice (# of pounds) given the budget constraint. graph these optimal quantities. draw your indifference curve on the same graph. c. Show on your graph what happens when the price of wild rice increases to $40 per pound. Find your new optimal quantities of noodles and wild rice. label all points on graph. label the…
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