5. Suppose the utility function for goods xand y is given by U (x, y) = xY + y(i). Calculate the uncompensated(Marshallian) demand functions for x and y,and describe how the demand curves for xand y are shifted by changes in I or the priceof the other good.(ii). Calculate the expenditure function for xand y.(iii). Use the expenditure function calculatedin part (b) to compute the compensateddemand functions for goods x and y.Describe how the compensated demandcurves for x and y are shifted by changes inincome or by changes in the price of theother good.

Answered: 5. Suppose the utility function for…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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If the utility function for a consumer is defined by U=6X^3/5Y^2/5 Given that the consumer's income is 300 currency units and unit price of goods X and Y are 12 and 15 currency units respectively, calculate the equilibrium quantity of both goods. Compute the price elasticity of demand for both goods and interpret your results. If income and prices of the two goods increase by 50%, calculate the equilibrium quantities of both goods
The utility function is given by u(x₁, x2) = min{2x1,5x2}. a) For this utility derive the demand functions x₁ (P₁, P2, 1) and x₂ (P₁, P2, 1). b) Set l=36 and p2 = 1. Draw the demand curve for good 1. c) Give the formula and draw the Engle curve for good 1. Is good 1 normal or inferior? Are preferences homothetic? Explain.
Consider a market with two goods, x and z. The consumer’s utility function is U = x^0.2z^0.8 A. Derive the demand function for x and z. B. Let ? = 2, = 4 and = 50. Find the equilibrium quantities demanded of x and z.
Q.7 A consumer's utility function is given by the expression: U = (0.6A"' + 0.47'"s} Determine the marginal utility functions for each commodity. Does marginal utility decrease when consumption increases? Assuming that the price of good X is Rs 15 and the price of Y is Rs 6, write the equation of the budget line and plot it when income is Rs 450. What is its slope? What does it indicate? Calculate the marginal rate of substitution of Y for X and interpret its economic meaning. Write the equation showing consumer's equilibrium condition. Obtain the equilibrium values of X and Y. Find the expressions for change in MUx due to increase in Y and change in MUy due to increase in X.
1) Max chooses to purchase movie tickets and restaurant meals every week with his $100. If the price of a movie ticket is $20 and the price of a restaurant meal is $25, then the slope of his budget constraint will be, a) 1/5 b) -1/5 c) 4/5 d) -4/5 2) Marginal rate of substitution(MRS) is the rate at which consumer is willing to trade one good for another. It must be true that: a) MRS is the slope of an indifference curve in reference to a particular bundle of goods. b) MRS is not the same along an indifference curve that is of usual shape. c) MRS is same along an indifference curve that is of usual shape. d) Both a) and b).
Please no written by hand solutions
Ricky has utility function u=x'y. This implies that MUx=2xy. MUy=x². His income is 100. The price of y is 10. (a) Find his demand for x at price 20. (b) Find his demand for x at price 30. (c) Write down his demand function for x: that is, write down his demand for x as a function of the price of x.
If the utility function for a consumer is defined by U=6X^0.6Y^0.7 . Given that the consumer's income is 300 currency units and unit price of goods X and Y are 12 and 15 currency units respectively, calculate the equilibrium quantity of both goods. Compute the price elasticity of demand for both goods and interpret your results. If income and prices of the two goods increase by 50%, calculate the equilibrium quantities of both goods
Consider a person who consumes two goods, x and y, and has a utility function given by U(x, y) = In(x)+y. This person has an income of $100 and faces a price of $0.50 for good x and $1 for good y. Price of x then rises to $0.60. Solve for the compensating variation (CV) and equivalent variation (EV) of this price change. Show your work.
A consumer has utility (see image) on ice creams (x) and cakes (y). (a) Are the indifference curves bowed towards the origin? (b) Derive his demand function (as a function of prices px, py and budget I) for ice cream (x). (c)(Looking at the demand function you found in (b), Is ice cream a normal good? Are ice cream and cakes substitutes or complements? Calculate the income elasticity of market demand at the point px = 2, py = 1 and I = 12.
Question 4 Naomi's expenditure function defined for a month for two commodities, Cassava (Q₁) and Banana (Q₂) is given by: 1. 11. Where P₁ is the price of Cassava (P₁>0), P2 is the price of banana (P₂ >0) and U is the fixed utility. The income of Naomi is m, where m > 0. Derive the indirect utility function for Naomi (Hint: Use the duality conditions) Using the Shephard's Lemma condition, derive Naomi's Hicksian demand function for Cassava (Q₁). iii. H IV. [125P,PU3 8 Using the Roy's identity, derive Naomi's Marshallian demand function for Banana (Q₂). Using the answer in (i), evaluate Naomi's maximum utility level when the price per tuber of Cassava is 5 cedis, the price per finger of banana is 10 cedis and her income is 250 cedis.

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