Suppose that we can represent Joyce's preferences for cans of pop (the x-good) and pizza slices (y-good) with the utility function min[4x,5y]. a) Find her Marshallian Demand Functions. b) Find her Hicksian Demand Functions
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Suppose that we can represent Joyce's preferences for cans of pop (the x-good) and pizza slices (y-good) with the utility function min[4x,5y].
- a) Find her Marshallian
Demand Functions. - b) Find her Hicksian Demand Functions
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- Assume you spend your entire income on two goods X & Y with prices given as PX & PY, respectively. Prices and income (I) are exogenous and positive. Given that U= X2Y 2 , derive the Hicksian demand function for good Y.The preferences of a typical Californian can be represented by the following utility function: U (x1 , x2 ) = α ln(x1) + (1 − α) ln(x2) Here, x1 and x2 are the quantities of electricity and gasoline, respectively. The consumer faces prices given by p1 and p2 and has income m. Currently, the government has decided to impose a consumption restriction so that any person in the state is allowed to consume at most 50 units of electricity (x1 ≤ 50). Call this restriction a rationing constraint. (a) If α=0.25, m=100,and p1 =p2 =1, find the optimal consumption bundle of gasoline and electricity. Is the electricity rationing constraint binding (meaning does x1∗ = 50)? (b) Suppose that α = 0.75, but the other parameters are the same. What is the optimal consumption bundle? Is the rationing constraint on electricity consumption binding? (c) Now, assume that there is no rationing constraint. Assume m = 100 and p1 = p2 = 1, but α remains as a generic parameter. Solve for the optimal quantity…Suppose that i’s preferences over goods x and y are represented by the following utility function Ui(x, y)=x^0.8·y^0.2. Let m denote the consumer’s income, p denote the price of good x and let the price of good y equal 1. a) Find the Marshallian demand functions for goods x and y. b) Show how each of the demand function is affected by a change in the price of good x. c) Which of the goods is an inferior good?
- Suppose a consumer’s utility function is u = x_1^(3/2) x_2^(3/2) . She spends her budget of £27 for two goods. The prices of both goods are p1 = 6 and p2 = 6. Derive the Marshallian demand functions for ?1 and ?2 as functions of both prices and income. Then find the optimal consumption point for the given budget constraint.Why the following variables (x1, x2 and x3) cannot be the Marshallian demandfunctions of a consumer with well–behaved preferences, even when pa ≥ pc.x1(p,y)= y/2pax2(p,y)= (pc y)/2pa pbx3(p,y)= (pa-pc)y/2pa pcHINT: Use properties of the Marshallian demand function to check this.Consider the following indirect utility function:ʋ(P,y) = y(P1r + P2r)-1/r Wherer = ρ/(ρ-1, Pi are parametric prices, and y is the consumer’s budget a) Solve for the Marshallian demand functions xi (P, y) and verify that these functions are homogenous of degree zero (Hint: you can also use Roy’s Identity). b) Derive the Hicksian demand functions xih (P,u)
- Suppose your utility for goods x1 and x2 is represented by the following utility function: U(x1,x2)= x11/5 x24/5 a) What is your marginal rate of substitution, MRS12? b) If the price for good x1 is p1 = 2, the price for good x2 is p2 = 4, and your available income is m = 20, write down your budget constraint. c) Using the prices and income given at b) above, find your optimal consumption choice bundle (Marshallian demand) and its corresponding utility level. d) Illustrate your optimal consumption choice on a graph. e) For the prices given in b), what income would you need to achieve a utility level of 25? PLEASE ONLY ANSWER PART C, D AND ESuppose your utility for goods x1 and x2 is represented by the following utility function: U(x1,x2)= x11/5 x24/5 a) What is your marginal rate of substitution, MRS12? b) If the price for good x1 is p1 = 2, the price for good x2 is p2 = 4, and your available income is m = 20, write down your budget constraint. c) Using the prices and income given at b) above, find your optimal consumption choice bundle (Marshallian demand) and its corresponding utility level. d) Illustrate your optimal consumption choice on a graph. e) For the prices given in b), what income would you need to achieve a utility level of 25?1. Consider a consumer who chooses bundles consisting of two commodities, x and y. Suppose that, regardless of the prices px and py (which are always positive), the consumer chooses to consume x and y in a ratio of 2:1. This behavior is consistent with: a. A consumer having Cobb-Douglas utility function. b. The consumer’s utility function exhibiting perfect complements. c. The consumer’s utility function exhibiting perfect substitutes. d. Any of the above could be correct.
- For each of the following utility functions, find the Marshallian demand function, the indirect utility function and the expenditure function. Assume that prices of x1 and x2 are p1 and p2 respectively and income is m. U(x1 x2) = In (x1 + x2) U(x1 x2) = x1 + x2Suppose a consumer in a competitive market maximises utility subject to a standard budget constraint. a. Given their resulting demand function, what assumptions would be required for one to conclude that when the price of good 1 goes up the consumer buys less of that good?b. Given their resulting demand function, what assumptions would be required for us to conclude that when the price of good 1 goes up the consumer buys more of good 2?Let x and y denote the amount of goods X and Y. Find the demand functions of X (do not need to find that of Y) when your preferences are represented by the utility function U = x + xy + y. Is X normal good? Can you confirm law of demand for X? What is the relationship of X with Y? Answer all of them by using the demand curve you derived
