Substitution and Income Effect (Calculation) Suppose that the consumer's utility function is Cobb-Douglas U(x; y) =...

Substitution and Income Effect (Calculation)

Suppose that the consumer's utility function is Cobb-Douglas U(x; y) = xy. She initially has $100

income and the prices that she faces are px = py = $2:

a. Compute her demands for x and y.

b. Now suppose that px decreases to $1 while py remains unchanged. Compute her new demands for x

and y.

c. What is the total (price) effect on the consumption of x?

d. What is the substitution effect (SE) and income effect (IE) due to the price change?

Solutions

Expert Solution

Rahul Sunny answered 1 year ago

Next > < Previous

Related Solutions

Suppose a consumer's utility function is given by U ( X , Y ) = X...

Suppose a consumer's utility function is given by U ( X , Y ) = X 1 2 Y 1 2. The price of X is PX=8 and the price of Y is PY=5. The consumer has M=80 to spend. You may find that it helps to draw a graph to organize the information in this question. You may draw in the blank area on the front page of the assignment, but this graph will not be graded. a) (2...

Assume a Cobb-douglas utility function of 2 goods x and y given by U = x...

Assume a Cobb-douglas utility function of 2 goods x and y given by U = x 0.5y 0.5 and an initial income I of 100. Let initial price be px = 4 and py = 1. Now vary the price of x from 1 to 7 in steps of 1. So you have 7 prices for x. px = {1, 2, 3, 4, 5, 6, 7} For each of these px, py REMAINS the SAME at 1. In the excel...

Consider the following Cobb-Douglas utility function: U(x,y) = 10 + 22xy, where x denotes the quantity...

Consider the following Cobb-Douglas utility function: U(x,y) = 10 + 22xy, where x denotes the quantity of apples and y denotes the quantity of pears. Income is m; the price for one apple is px and the price for one pear is py. b) By applying the Lagrangian method, derive the optimal demands for apples and pears. c) What is the impact of an increase in the price of apples on the optimal demand for pears? What is the impact...

Consider the following utility function U(x,y)=x^r+y^r,0<r<1 Find the income effect and substitution effect? ...

Consider the following utility function U(x,y)=x^r+ y^r,0<r<1 Find the income effect and substitution effect? Does the substitution effect increase or decrease when r increases?

A consumer's preferences for food (x) and clothes (y) are represented by the utility function u(x,y)=...

A consumer's preferences for food (x) and clothes (y) are represented by the utility function u(x,y)= x + 2 ln(y). The prices of food and clothes are px and py euros/unit, respectively, and the consumer's income is I euros. A. (10 points) Describe the consumer's problem, including her budget constraints, and calculate her ordinary demand functions, x(px,py,I) and y(px,py,I). B. (10 points) For prices and income (px,py,I)=(1,1,3), calculate the substitution and income effects over the demand of y of a...

Marvin has a Cobb-Douglas utility function, U=q10.5q20.5 his income is Y=$900, and initially he faces prices...

Marvin has a Cobb-Douglas utility function, U=q10.5q20.5 his income is Y=$900, and initially he faces prices of p1=$44 and p2=$2. If p1 increases from $4 to $5, what are his compensating variation (CV), change in consumer surplus (ΔCS), and equivalent variation (EV)? Marvin's compensating variation (CV) is $nothing. (Enter your response rounded to two decimal places and include a minus sign if necessary.) Marvin's change in consumer surplus (Upper DeltaΔCS) is $nothing. (Enter your response rounded to two decimal places...

Which of the following utility functions is a Cobb-Douglas? Group of answer choices U(x,y) = ln(x)...

Which of the following utility functions is a Cobb-Douglas? Group of answer choices U(x,y) = ln(x) + 4y U(x,y) = 2x + 4y U(x,y) = ln(x) + 4ln(y) U(x,y) = min{x, 4y} None of the above

III. A common utility function used to illustrate economic examples is the Cobb-Douglas function where U(X,...

III. A common utility function used to illustrate economic examples is the Cobb-Douglas function where U(X, Y)= XαYβ, where α and β are decimal exponents that sum to 1.0 (for example, 0.3 and 0.7). a. For this utility function, the MRS is given by MRS = MUX=MUY = αY/βX. Use this fact together with the utility-maximizing condition (and that α+ β =1) to show that this person will spend the fraction of his other income on good X and the...

Suppose a consumer's preferences are given by U(X,Y) = X2*Y. Thus, the marginal utility of X,...

Suppose a consumer's preferences are given by U(X,Y) = X2*Y. Thus, the marginal utility of X, MUx = 2XY and the marginal utility of Y, MUy = X2. Suppose the consumer has $180 to spend and the price of good Y is $1. Sketch the price-consumption curve for the prices of Px = $1 Px = $2 Px = $3 To do this, carefully draw the budget constraints associated with each of the prices for good X, and indicate the...

Suppose that the utility function of a consumer is U(x,y) = x ¼y ¾, where x...

Suppose that the utility function of a consumer is U(x,y) = x ¼y ¾, where x and y are the quantities of the good X and good Y consumed, respectively. The consumer's income is 400. (a) What is the demanded bundle when the price of good X is 10 and the price of good Y is 10? (b) Redo part (a) when the price of good X is doubled? (c) Redo part (a) when the price of good Y is...

Subjects