A consumer of two goods has utility u(x₁, x2) = 12. She can purchase each good i = 1,2 at a price of p; dollars per unit. Alternatively, she can buy a discount card for fixed fee of c dollars that allows her to purchase good 1 at a price of p₁/2 dollars per unit. (The discount card has no effect on the price of good 2.) The discount card is of no value to the consumer except insofar as it reduces the price she pays for good 1. Find this consumer's Marshallian demand for each c> 0. Solution: If w

A consumer of two goods has utility u(x₁, x2) = 12. She can purchase each good i = 1,2 at a price of p; dollars per unit. Alternatively, she can buy a discount card for fixed fee of c dollars that allows her to purchase good 1 at a price of p₁/2 dollars per unit. (The discount card has no effect on the price of good 2.) The discount card is of no value to the consumer except insofar as it reduces the price she pays for good 1. Find this consumer's Marshallian demand for each c> 0. Solution: If w

Microeconomics A Contemporary Intro

10th Edition

ISBN:9781285635101

Author:MCEACHERN

Publisher:MCEACHERN

Chapter6: Consumer Choice And Demand

Section: Chapter Questions

Problem 8QFR

See similar textbooks

Similar questions

Juliana gets the following 15 units for free if she buys 30 units of good Y (at RM2 per unit). This promotion is only valid for the first 30 pieces she purchases. Calculate Julia's total utility received. Derive Juliana's new budget line equation. Sketch the budget line before and after the change in the price of good Y using an appropriate diagram.
Indicate whether the statement is true or false, and justify your answer.There is a massive body of evidence that humans prefer a fixed amount of utility now to that same amount of utility later.
Casper consumes cocoa and cheese. Cocoa is sold in an unusual way. There is only one supplier, and the more cocoa you buy from him, the lower the price you have to pay per unit. In fact, x2x2 units of cocoa will cost Casper √x2x2 dollars. Cheese is sold in the usual way at a price of $2 per unit. Casper's income is $10 and his utility function is u(x1,x2)=x21x2u(x1,x2)=x12x2, where x1x1 is his consumption of cheese and x2x2 is his consumption of cocoa. (1) Sketch Casper's budget set. (2) Sketch some of his indifference curves. (3) Calculate the amount of cheese and the amount of cocoa that Casper demands at these prices and this income. Do not forget to check the corners. (Hint: Write down the Lagrangean for this problem and solve the maximization program
You are given the following utility function and price of commodities q1 and q2: U = 3q1+q1q2-5q2-15 P1=3 and p2=2 If the corresponding bugdet is 20. i. Write the consumer's budget equation,augmented objective function, ii.construct a constrained utility maximization problem out of the information given above, Is the second order condition for a maximum satisfied? Iii. Find the optimum level of U and the levels of q1 and q2 that will satisfy the first order condition for a maximum.
The following data pertain to products A and B, both of which are purchased by Madame X. Initially, the prices of the products and quantities consumed are: PA = $10, QA = 3, PB = $10, QB = 7. Madame X has $100 to spend per time period. After a reduction in price of B, the prices and quantities consumed are: PA = $10, QA = 2.5, PB = $5, QB = 15. Assume that Madame X maximizes utility under both price conditions above. Also, note that if after the price reduction enough income were taken away from Madame X to put her back on the original indifference curve, she would consume this combination of A and B: QA = 1.5, QB = 9 Determine the change in consumption rate of good B due to (1) the substitution effect and (2) the income effect. Determine if product B is a normal, inferior, or Giffen good. Explain.
Q50 Marginal utility analysis predicts a downward-sloping demand curve for good X because... a. As PX rises, the consumer increases purchases of X such that MUX/PX is equal to MU/P for all other products. b. As PX falls, the ratio MUX/PX becomes smaller, causing the consumer to purchase more of good X. c. As PX falls, the consumer increases purchases of X until MUX/PX is equal to MU/P for all other products. d. Utility-maximising consumers equate the marginal utility received for each product consumed. e. All demand curves are downward sloping, regardless of the behaviour of consumers.
True/False Utility refers to the total satisfaction or happiness that an individual get from consuming a product.
Q1-Select the true or false for the following statement also give the explanation and support your answer with graphical presentation where necessary. Explanation is compulsory 3 to 6 line. If total utility at optimum level marginal utility is negative.
Max’s preferences can be represented by the utility function u(x1, x2) = 2√ x1 + x2. Take good 2 to be the numeraire (p2 = 1). a) For any price p1 and income m, write down and solve his utility maximization problem, i.e. find the demand x1(p1, m) and x2(p1, m) using the Lagrangian method (assuming an interior solution). Illustrate why this method is equivalent to using the two conditions (1) |MRS| =price ratio and (2) Budget constraint. b) In doing so, also solve for λ ∗ . c) Given any p1 and income m, find the utility of Max corresponding to his demand. Denote this by v(p1, m). That means, find v(p1, m) = u(x1(p1, m), x2(p1, m)). d) To understand how v(p1, m) changes with m, i.e. compute ∂v(p1,m) ∂m . Compare with your answer to b).
Find the maximizing utility for the person consuming two commodities from the following information: Income: 10 OMRPrice of Qx= 2 OMR, Price of Qy= 1 OMR
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)
33. Suppose MRSx,y = MUx/MUy = 0.1(a) If the consumer substitutes 10 units of X for one unit of Y, then the utility remainsunchanged(b) Regardless of prices, the consumer will only consume Y(c) If the consumer substitutes 1 unit of Y for 0.1 unit of X, then the utility remainsunchanged(d) Regardless of prices, the consumer will only consume X