Define the Marginal Rate of Substitution between two goods (X and Y). If a consumer’s preferences are given by U(X,Y) = X1/4Y 3/4, compute the consumer’s marginal rate of substitution as a function of X and Y. Calculate the MRS if the consumer has chosen to consumer 12 units of X and 30 units of Y.

Define the Marginal Rate of Substitution between two goods (X and Y). If a consumer’s preferences are given by U(X,Y) = X1/4Y 3/4, compute the consumer’s marginal rate of substitution as a function of X and Y. Calculate the MRS if the consumer has chosen to consumer 12 units of X and 30 units of Y.

Micro Economics For Today

10th Edition

ISBN:9781337613064

Author:Tucker, Irvin B.

Publisher:Tucker, Irvin B.

Chapter6: Consumer Choice Theory

Section6.A: Indifference Curve Analysis

Problem 1SQP

See similar textbooks

Similar questions

Kate’s utility function includes coffee (c) and sugar (s). She only consumes coffee and sugar together, and she only consumes in the ratio of one unit (cup) of coffee with two units (spoons) of sugar. Her utility function is What is her marginal utility of sugar if she has 4 cups of coffee and 6 spoons of sugar? Remember that unit are infinitely divisible (you can have parts of units). (a) 0 (b) 1 (c) ½ (d) 2
QUESTION 1 Let qa be the quantity of apples and qo the quantity of oranges. A consumer's utility is described by the function u(qA.90)= 39A + 590 This consumer curently consumes 2 apples and 4 oranges. For this consumer, the marginal utilities are MUA= and MUO= Moreover, the marginal rate of substitution is MRSA O=
It is common for supermarkets to carry both generic (store-label) and brand-name (producer-label) varieties of sugar and other products. Many consumers view these products as perfect substitutes, meaning that consumers are always willing to substitute a constant proportion of the store brand for the producer brand. Consider a consumer who is always willing to substitute 4 pounds of a generic store brand for 2 pounds of a brand-name sugar. Do these preferences exhibit a diminishing marginal rate of substitution? Assume that this consumer has $24 of income to spend on sugar, and the price of store-brand sugar is $1 per pound and the price of producer-brand sugar is $3 per pound. How much of each type of sugar will be purchased? How would your answer change if the price of store-brand sugar was $2 per pound and the price of producer-brand sugar was $3 per pound?
Find the marginal utility (MU) and marginal rate of substitution (MRS) of following utility functions. 1. U(x1,x2)=ln(x1)+x2,findMUx1,MUx2,andMRS(x1,x2) 2. U(x1,x2)=(2x21+x32)1/2,findMUx1,MUx2,andMRS(x1,x2)
Charlie's utility function is (1-a) U(xa, XB) = Ax“xr-) where A > 0 and a > 0
Consider the following utility function. U=U(X,Y)=X0.2Y0.8 Find the marginal utilities. Determine their signs. Provide the economic interpretation of the signs of these marginal utilities. Determine whether the law of diminishing marginal utility holds for both goods.
Anna has an income of 1000 euros and utility function U(x,y)=x²y³. The prices of the two goods are P₁=5 and Py-20. a) Define the budget constraint and represent it graphically. (
Utility is given by the function U(x,y) = x0(y + 4)0.3. a. Calculate the marginal utility of x in terms of x and y. Simplify. b. Calculate the marginal utility of y in terms of x and y. Simplify. c. Calculate the marginal rate of substitution in terms of x and y. Simplify.
suppose a consumer consumes two goods x and y with utility function u=x^0.5+y^1.5, does the utility funciton exhibit diminishing marginal utility for (i) x (ii)y?
Assume a consumer with the utility functionU(X,Y)=X²Y²and the typical budget constraintM= PxX+ PyY a. Derive the consumer’s demand for X and Y in terms of the parameters.b. If income of the consumer is 100, price of X is 2 and price of Y is 4, what the quantities of X and Y that gives the consumer maximum satisfaction?c. What is the consumer’s marginal rate of substitution between X and Y
1 Marginal utility and marginal rate of substitution Suppose an individual who derives utility u(x, y) from consuming a units of good X and y units of good Y. For each of the following utility functions, derive the marginal utility of good X, the marginal utility of good Y, and the marginal rate of substitution between X and Y. (A) u(x, y) = x+by¹/3 (B) u(x, y) = (xy) (C) u(x, y) = ax + xy + by² (D) u(x, y) = n(ax + y) 1 (E) u(x, y) = (x² + √y²) = 2
Questions 1. Will's utility from vacations (91) and meals (92) is given by the function U(V, M) = 91 x 92. Last year, the price of vacations was $200 and the price of meals was $50. This year, the price of meals rose to $75, while the price of vacations remained the same. Both years, Will had an income of $1500. (a) What is the compensating variation for the price change in meals? (b) What is the equivalent variation for the price change in meals?