Marvin has a Cobb-Douglas utility function, U=91 0.5. 0.5 92 his income is Y = $900, and initially he faces prices of p, = $2 and p2 $1. If p1 increases from $2 to $5, what are his compensating variation (CV), change in consumer surplus (ACS), and equivalent variation (EV)? Marvin's compensating variation (CV) is $ (Enter your response rounded to two decimal places and include a minus sign if necessary.)

Marvin has a Cobb-Douglas utility function, U=91 0.5. 0.5 92 his income is Y = $900, and initially he faces prices of p, = $2 and p2 $1. If p1 increases from $2 to $5, what are his compensating variation (CV), change in consumer surplus (ACS), and equivalent variation (EV)? Marvin's compensating variation (CV) is $ (Enter your response rounded to two decimal places and include a minus sign if necessary.)

Micro Economics For Today

10th Edition

ISBN:9781337613064

Author:Tucker, Irvin B.

Publisher:Tucker, Irvin B.

Chapter6: Consumer Choice Theory

Section: Chapter Questions

Problem 16SQ

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Marvin has a Cobb-Douglas utility function, 0.5 0.5 U=91 92 his income is Y = $300, and initially he faces prices of p₁ = $1 and p2 = $1. If p₁ increases from $1 to $5, what are his compensating variation (CV), change in consumer surplus (ACS), and equivalent variation (EV)? Marvin's compensating variation (CV) is $ (Enter your response rounded to two decimal places and include a minus sign if necessary.)
C.16.
Suppose that Lucy's quasilinear utility function is U=2(9₁) 0.5 +4₂₁ with p₁ = $4 and p₂ = $2 initially and p, increasing from $4 to $5. Compare her compensating variation (CV), equivalent variation (EV), and change in consumer surplus (ACS). Lucy's compensating variation (CV) is $0.20. (Enter your response rounded to two decimal places and include a minus sign if necessary.) Lucy's equivalent variation (EV) is $0.20. (Enter your response rounded to two decimal places and include a minus sign if necessary.)
Leo's utility function is U=min(3x,9.1y). If Leo's income is 171.1 dollars, the price of good X is 4 and the price of good Y is 6.2, what is Leo's maximum utility?
Greg has the following utility function: u=x053x047. He has an income of $64.00, and he faces these prices: (p₁.pz) = (3.00,4.00). Suppose that the price of x₁ increases by $1.00. Calculate the compensating variation for this price change. Give your answer to two decimals.
14.3 (0) Quasimodo consumes earplugs and other things. His utility function for earplugs x and money to spend on other goods y is given by u(x, y) = 100x 2:² 2 +y. (a) What kind of utility function does Quasimodo have? (b) What is his inverse demand curve for earplugs?. (c) If the price of earplugs is $50, how many earplugs will he consume? (d) If the price of earplugs is $80, how many earplugs will he consume? (e) Suppose that Quasimodo has $4,000 in total to spend a month. What is his total utility for earplugs and money to spend on other things if the price of earplugs is $50?
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QUESTION 3 Consider an individual who has a utility function U(X,Y) = 2x1/2) + Y/2), the prices of goods X and Y are given by px = $8 and pY = $2, and the income level of consumer is I = $80. 3-a) Write the consumer's utility maximization probiem (formally, as we wrote in the lectures). 3-b) Write the Lagrangian function associated to the maximization problem. 3-c) Write the first order conditions (FOC). 3-d) Find the consumption bundle that maximizes consumer's utility.
0.8 A consumer's utility function is given by the expression: U = (0.6X0.5 +0.4Y0.5) ². 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.
You consume music (M) and concert tickets (C). Your utility function is U(M, C) = M1/4C3/4. The marginal utility for concert tickets, MUC is MUC =3/4C-1/2M1/4 and the marginal utility for music, MUM is MUm = 1/4C3/4M-3/4 (a) Calculate MRSMC using only the given marginal utilities. (b) Solve for the utility of bundle A where M = 16 and C = 16. Solve for your utility at bundle B where M = 128 and C = 8. Are the utilities the same? (c) Calculate MRSMC at bundle A and at bundle B. Are they the same? (d) Are your indifference curves convex? Draw the ICs. Make sure to label the quantities of the consumption bundles, the axis, and the MRS at those bundles.
• Question #20: While visiting family in Mexico, your professor has a budget of $ 304 ($ = pesos) that he spends on tacos and tequila. The price of tacos is $ 14 and a shot of tequila is priced at $ 12. During his visit the price of tacos changes to $ 14 . Assume your professor has a Cobb-Douglas utility function with (tacos) parameter a = ( 29/ 100 ). What is the substitution effect on purchases of tacos ? (Assume both goods are commodities.)
Assume, as in Exercise 22.1, that a consumer has utility function F or fruit and chocolate. Determine the consumer's demand functions q1(P1, P2, M) and q2(P1, P2, M). Determine also It* in terms of P1, P2 and M. Find the indirect utility function and show that It* = 8Vj8M. Suppose, as before, that fruit costs $1 per unit and chocolate $2 per unit. If the income is raised from $36 to $36.5, determine the precise value of the resulting change in the indirect utility function. Show that this is approximately equal to (O.5)λ*, where λ* is evaluated at P1 = 1,P2 = 2 and M = 36. Exercise 22.1 A consumer purchases quantities of two commodities, fruit and chocolate, each month. The consumer's utility function is For a bundle (X1, X2) of X1 units of fruit and X2 units of chocolate. The consumer has a total of $49 to spend on fruit and chocolate each month. Fruit cost $1 per unit and chocolate costs $2 per unit. How many units of each should the consumer buy…