Question

In: Economics

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?

Expert Solution

Solution:

Given

a)

Let find the substitution effect first

Substitution effect = change in quantity of x with change in quantity of Y.

Now,

Now applying y/x constant lets assume r increases

then

The substitution effect decreases with increase in r.

b)

Now considering income effect

Now,

Similarly,

Rahul Sunny answered 2 years ago

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...

utility function u(x,y;t )= (x-t)ay1-a x>=t, t>0, 0<a<1 u(x,y;t )=0 when x<t does income consumption curve...

utility function u(x,y;t )= (x-t)ay1-a x>=t, t>0, 0<a<1 u(x,y;t )=0 when x<t does income consumption curve is y=[(1-a)(x-t)px]/apy ?(my result, i used lagrange, not sure about it) how to draw the income consumption curve?

Jim’s utility function is U(x, y) = xy. Jerry’s utility function is U(x, y) = 1,000xy...

Jim’s utility function is U(x, y) = xy. Jerry’s utility function is U(x, y) = 1,000xy + 2,000. Tammy’s utility function is U(x, y) = xy(1 - xy). Oral’s utility function is -1/(10 + xy. Billy’s utility function is U(x, y) = x/y. Pat’s utility function is U(x, y) = -xy. a. No two of these people have the same preferences. b. They all have the same preferences except for Billy. c. Jim, Jerry, and Pat all have the same...

1. Consumer’s utility function is: U (X,Y) = 10X + Y. Consumer’s income M is 40...

1. Consumer’s utility function is: U (X,Y) = 10X + Y. Consumer’s income M is 40 euros, the price per unit of good X (i.e. Px ) is 5 euros and the price per unit of good Y (i.e. Py) is 1 euro. a) What is the marginal utility of good X (MUx) for the consumer? b) What is the marginal utility of good Y (MUy) for the consumer? How do I calculate these?

1. In the utility function U(x,y)=x^5y^2 does Y exhibit diminishing marginal rate of substitution? Please show...

1. In the utility function U(x,y)=x^5y^2 does Y exhibit diminishing marginal rate of substitution? Please show your work. 2.What is the no-waste condition for the utility function U(x,y)=min{x/3,y/5} express your answer in terms of y as a function of x 3. What is the MRS of the utility function U(x,y)=3x+1/2y? please show your work

Given the utility function U ( X , Y ) = X 1 3 Y 2...

Given the utility function U ( X , Y ) = X 1 3 Y 2 3, find the absolute value of the MRS when X=10 and Y=24. Round your answer to 4 decimal places.

Consider the utility function, U(x,y) = ln(x) + y. Please answer the following questions, showing all...

Consider the utility function, U(x,y) = ln(x) + y. Please answer the following questions, showing all work. (1) Derive an expression showing the overall effect of an increase in py on the quantity of y consumed, holding constant px and income (I). (2) Now, show how that overall effect in (1) can be decomposed into a separate substitution effect and income effect. Show these effects explicitly. (3) Now, do the same for x: derive an expression showing the overall effect...

Consider a consumer with the utility function U(X, Y) = X^2 Y^2 . This consumer has...

Consider a consumer with the utility function U(X, Y) = X^2 Y^2 . This consumer has an income denoted by I which is devoted to goods X and Y. The prices of goods X and Y are denoted PX and PY. a. Find the consumer’s marginal utility of X (MUX) and marginal utility of Y (MUY). b. Find the consumer’s marginal rate of substitution (MRS). c. Derive the consumer's demand equations for both goods as functions of the variables PX,...

Esther consumes goods X and Y, and her utility function is U(X,Y)=XY+Y For this utility function,...

Esther consumes goods X and Y, and her utility function is U(X,Y)=XY+Y For this utility function, MUX=Y MUY=X+1 a. What is Esther's MRSXY? Y/(X + 1) X/Y (X + 1)/Y X/(Y + 1) b. Suppose her daily income is $20, the price of X is $4 per unit, and the price of Y is $1 per unit. What is her best choice? Instructions: Enter your answers as whole numbers. X = Y = What is Esther's utility when her...

Consider the following utility function: U(x, y) = 10x + 2y. A consumer faces prices of...

Consider the following utility function: U(x, y) = 10x + 2y. A consumer faces prices of px = 1 and py = 2. Assuming that graphically good x is on the horizontal axis and good y is on the vertical axis, suppose the consumer chooses to consume 5 units of good x and 13 units of good y. What is the marginal rate of substitution (MRS) equal to?