Answered: 1. The utility function for an… | bartleby

Microeconomic Theory

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter5: Income And Substitution Effects

Section: Chapter Questions

Problem 5.5P

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1. The utility function for an individual is given by the equation: U = X1 0.25X2
0.75 and their budget constraint is P1x1 + P2X2 = M (1) Using the Lagrange,
and showing all work, Derive the demand functions for good X1 and good X2
(ii) Given that the price for good 1, p1= k2.5 and the price for good 2, p2=k5,
and the consumer's income is k100. Calculate and graphically present the
optimal choice for good 1 and good 2

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The utility function for an individual is given by the equation: U = X1 0.25X2 0.75 and their budget constraint is P1X1 + P2X2 =M (i) Using the Lagrange, and showing all work, Derive the demand functions for good X1 and good X2 (ii) Given that the price for good 1, p1= k2.5 and the price for good 2, p2=k5, and the consumer’s income is k100. Calculate and graphically present the optimal choice for good 1 and good 2
An individual has $12 dollars to spend on the two goods (y=12). The price of good #1 is $2 (p1=2) and the price of good #2 is $6 (p2=6). How much of good #1 will the individual demand and how much of good #2 will the individual demand if their utility function is given by the following expression: U (q1 , q2) = q1 +2q2 a.) Quantity demanded of good #1 = b.) Quantity demanded of good #2 =
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 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 E
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?
Lea's utility function is U =0.7 ln( x ) + y where x denotes her consumption of good X and y denotes her consumption of good Y. Suppose the government imposes a per-unit tax on good X equal to 5 dollars. The price of good X charged by the sellers of good X is Px = 9 (and does not change due to the tax), the price of good Y is Py = 13 and Lea's income is M = 389. What is Lea's own-price substitution effect of the price increase due to the tax ?
1. 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 = X2 + Y2 , derive the Marshallian demand function for good Y and evaluate the type of good. 2. 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= X2Y2 , derive the Hicksian demand function for good Y.3. Suppose that initially PX = 2, PY = 8, I = 96 and the Marshallian demand function for good Y is given by Y∗ = (0.5I/ PY)+(0.5PX/PY)− 0.5. Calculate the own price & income elasticities of demand for good Y. Interpret your computed values and say something about the type of good.4. Suppose the economy has 100 units each of goods X and Y and the utility functions of the (only) 2 individuals are: UA (XA,YA) = X0.25Y0.75, UB (XB,YB) = X0.75Y 0.25Show that pareto-improvement is possible if,…
An individual's utility is given by: U (q1, q2) = a(q1)+ b(q2), where a and b are constants. When prices are P1= 4 and P2=1, the individual can only maximize utility by purchasing all good #2. When the prices are P1=3 and P2=1, the individual can only maximize utility by consuming all good #1. Which of the following statements below must be true? A. Goods #1 and #2 are complements B. a < b C. 3 < a/b <4 D. The indifference curves exhibit diminishing MRS
Suppose a consumer’s preferences for goods Y and X can be represented by the utility function, U(X,Y)=X2Y. The consumer's budget constraint is M=PxX+PyY where Px is the price of the good X, Py is the price of Y, and M represents income. Derive the demand equations for the two goods.
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 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
The market for lemon has 10 potential consumers ,each having an individual demand curve p=101-10Q where p is price in dollars per cup and Q is the number of cups demanded per week by the ¡th consumer.find the market demand curve using algebra . Draw an individual demand curve and the Market demand curve . What is the quantity demanded by each customer and in the market as a whole when lemon is priced at p=$1/cup?

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