Lea's utility function is U = In(x) + 0.8 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 2 dollars. The price of good X charged by the sellers of good X is Px = 7 (and does not change due to the tax), the price of good Y is Py = 14 and Lea's income is M = 338. What is Lea's own-price substitution effect of the price increase due to the tax ?

Lea's utility function is U = In(x) + 0.8 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 2 dollars. The price of good X charged by the sellers of good X is Px = 7 (and does not change due to the tax), the price of good Y is Py = 14 and Lea's income is M = 338. What is Lea's own-price substitution effect of the price increase due to the tax ?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.11P

See similar textbooks

Similar questions

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 ?
Lan's utility function is U = xa y1-a where x denotes her consumption of good X, y denotes her consumption of good Y and a = 0.8. The price of good X is Px = 7, the price of good Y is Py = 14 and Lan's income is M = 338. If each price increases by 2 dollars, how much money must Lan be given to compensate her for the price increase?
1. John consumes good X and good Y. His expenditure function is E=2U(PX)^5(PY)^5. His demand for goods X and Y are given by X=I/(2 PX), Y= I/(2 PY) Suppose that initial PX=1 and PY=1. John's income is 12. a. Find John's initial level of utility. b. Suppose the government announces plans to introduce a tax of 3 per unit on good X. Find an exact expression for the amount of income John would be just willing to give up to avoid the tax on good X. c. Suppose the government implements the tax. How does John's consumption of good X change? Find the income and substitution effects (with regards to good X) associated with the tax increase.
The utility function of a consumer is u = √x + 2y. (a) Show mathematically that the rise of Px will decrease demand for x goods. (b) Demonstrate mathematically that an increase in Px will increase demand for goods y. (c) If currently the price of goods is four times more expensive than the price of goods x and the government wants to set a tax that results in the increase in Px′ = 1.1Px, what are the units of decrease in the number of x items requested?
Part 1) An individual utility function is given by U(x,y) = x·y. Derive this individual indirect utility function. Using this individual indirect utility function, compute her level of utility when I = $800, px = $20 and py = $40. It is equal to 200 utils. Part 2) An individual utility function is given by U(x,y) = x·y. Let I = $800, px = $20 and py = $40. Suppose that a tax t of $10 per unit is imposed on good x. Assume that the full burden of this excise tax is borne by this consumer, i.e. the new price this individual faces for good x is p’x = px + t = $20+ $10 = $30. Use the indirect utility function you derived earlier to compute this person new utility level with this excise tax. It is equal to 133.33 utils. Question: An individual utility function is given by U(x,y) = x·y. Let I = $800, px = $20 and py = $40. Suppose that a tax t of $10 per unit is imposed on good x. Assume that the full burden of this excise tax is borne by this consumer, i.e. the new price this individual…
Pankti consumes two goods, x and y. Her utility function is given byU(x, y) = ln(xy).(a) Suppose when Pankti’s income is 12, her optimal bundle consists of 2 units of x and 6units of good y. Without solving for Pankti’s Marshallian demands for x and y,determine how her consumption of x and y would change if her income doubled(holding constant the prices of the goods). Justify your answer as well as you are able.(b) Find an expression for Pankti’s indirect utility function, V (px, py, m), using themethod of Lagrange multipliers. Confirm your answer to part (b) using theMarshallian demands you derive in the process of solving the optimization process.(c) Suppose the price of good x is 2 and the price of good y is 2. Find Pankti’s utilitywhen her income is 24. Now suppose the price of good x doubles to 4. How much extraincome does Pankti need to obtain the same level of utility she had prior to the priceincrease?
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
Suppose that Sam has a utility function u(x, y)= xy2 where x is the amount of good 1 and y is the amount of good 2. The price of good 1 is $10 and price of good 2 is $20, and the income is $ 90. The price of good 1 is denoted by px and the income is donated by m. Derive the equations for income-offer curve, Engel curve for good 1, demand curve for good 1 and solve for the optimal consumption of (x, y).
Sam's is interested in two goods, X and Y. His indirect utility function is U* = M px-0.8 py0.8-1. ( same as U* = M /(px0.8 py1-0.8 ) ) where M is Sam's income, and px and py denote respectively the price of good X and the price of good Y. Sam's market demand function for good X is X*=0.8M/px . Find the absolute value of the change in Sam's consumers surplus if the price of good X rises from 1 to 4 dollars due to a per-unit tax imposed by the government, assuming his income is M=514 and price of good Y is equal to 4.
A consumer’s utility only depends on the consumption of goods A and B according to the following Cobb-Douglass utility function: U(A, B) = A1/4 B 3/4. The price of goods A and B are $20 and $40, respectively. The consumer has a budget of $1200 that he can use to consume the two goods. a. Write down the budget constraint and plot it. b. Calculate the optimal bundle and maximized utility for the consumer. c. A new tax of $10 is imposed on the price of good B. Compute the new optimal bundle of good A and B for the same consumer. What is the utility loss due to the tax? d. Show that the consumer would prefer a lump sum income tax that raises the same revenue as the tax on good B. Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.
A consumer has a utility function U (C₁, C₂) and her expenditure function is E = P₁C₁ + P₂C₂ where the prices of goods one and two are p₁ and p2 respectively. She wants to find the minimum level of expenditure, E* (P₁, P2, U), that allows her to achieve a certain level of utility U, i.e., so that U(C₁, C₂) ≥ U. Suppose that U(C₁, C₂) = (c₁)^(1/2)+ a(c₂)^(1/2) a) will constraint U(C₁, C₂) ≥ U bind. And what is the langranian for this problem B)Write down the Lagrangian conditions and find the ratio C1/C2 in terms a,p1or p2 C)Assume that a=1,p1 = pand p2 =1.Find C1 and C2. Substituting these values into the expenditure function, find E*(p, Ū), the minimum level of expenditure required to achieve the required level of utility Ū. Use this to prove thatdE*/dp = C1
Individual that consumes two goods (X and Y) and has a CES Utility Function of the form: U = 100(X^(0.75) + Y^(0.75)). Income of 1000, the price of Good X is 10 and the Price of Good Y is 20 a) Find the Marginal Rate of Substitution as a function of the quantities consumed of Good X and Good Y. b) Write out the Lagrangian for this problem. c) Solve to find the demand for Good X, the demand for Good Y, and the highest level of utility for this individual. d) Now consider an increase in the price of Good X to 20. What is the demand for Good X and Good Y? What is the Utility of the consumer following the price change? e) Considering the change in demand for each good between parts c) and d), how much is due to the substitution effect and how much is due to the income effect? f) Show your answers on a graph.