Question

Suppose a consumer’s utility function is given byU(X, Y) =X^1/2 Y^1/2. Also, the consumer has $30...

Suppose a consumer’s utility function is given byU(X, Y) =X^1/2 Y^1/2. Also, the consumer has $30 to spend. The price of X,PX= $3, and the price of Y,PY= $5.

a) (4 points) How much X and Y should the consumer purchase in order to maximize their utility?

b) (4 points) How much utility does the consumer receive?

c) (4 points) Now suppose PX increases to$6. What is the new bundle of X and Y that the consumer will demand?

How much money would the consumer be willing to pay to avoid the price increase? Is thiscompensating variation or equivalent variation?

e) (4 points) How much additional money would the consumer need in order to have the same utilitylevel after the price change as before the price change? Is this compensating variation or equivalentvariation?

f) (4 points) Of the total change in the quantity demanded of X, how much is due to the substitutioneffect and how much is due to the income effect? Note: since there is an increase in the price of GoodX, these values will be negative.

Business   Economics   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Suppose a consumer’s utility function is given by U(X,Y) = X*Y. Also, the consumer has $360...
Suppose a consumer’s utility function is given by U(X,Y) = X*Y. Also, the consumer has $360 to spend, and the price of X, PX = 9, and the price of Y, PY = 1. a) (4 points) How much X and Y should the consumer purchase in order to maximize her utility? b) (2 points) How much total utility does the consumer receive? c) (4 points) Now suppose PX decreases to 4. What is the new bundle of X and...
Suppose a consumer’s Utility Function U(x,y) = X1/2Y1/2. The consumer wants to choose the bundle (x*,...
Suppose a consumer’s Utility Function U(x,y) = X1/2Y1/2. The consumer wants to choose the bundle (x*, y*) that would maximize utility. Suppose Px = $5 and Py = $10 and the consumer has $500 to spend. Write the consumer’s budget constraint. Use the budget constraint to write Y in terms of X. Substitute Y from above into the utility function U(x,y) = X1/2Y1/2. To solve for the utility maximizing, taking the derivative of U from (b) with respect to X....
3. Suppose that a consumer has a utility function given by U(X,Y) = X^.5Y^.5 . Consider...
3. Suppose that a consumer has a utility function given by U(X,Y) = X^.5Y^.5 . Consider the following bundles of goods: A = (9, 4), B = (16, 16), C = (1, 36). a. Calculate the consumer’s utility level for each bundle of goods. b. Specify the preference ordering for the bundles using the “strictly preferred to” symbol and the “indifferent to” symbol. c. Now, take the natural log of the utility function. Calculate the new utility level provided by...
Suppose a consumer has the utility function U (x, y) = xy + x + y....
Suppose a consumer has the utility function U (x, y) = xy + x + y. Recall that for this function the marginal utilities are given by MUx(x,y) = y+1 and MUy(x,y) = x+1. (a) What is the marginal rate of substitution MRSxy? (b)If the prices for the goods are px =$2 and py =$4,and if the income of the consumer is M = $18, then what is the consumer’s optimal affordable bundle? (c) What if instead the prices are...
Consider a consumer whose utility function is u(x, y) = x + y (perfect substitutes) a....
Consider a consumer whose utility function is u(x, y) = x + y (perfect substitutes) a. Assume the consumer has income $120 and initially faces the prices px = $1 and py = $2. How much x and y would they buy? b. Next, suppose the price of x were to increase to $4. How much would they buy now?    c. Decompose the total effect of the price change on demand for x into the substitution effect and the...
A consumer has utility function U(x, y) = x + 4y1/2 . What is the consumer’s...
A consumer has utility function U(x, y) = x + 4y1/2 . What is the consumer’s demand function for good x as a function of prices px and py, and of income m, assuming a corner solution? Group of answer choices a.x = (m – 3px)/px b.x = m/px – 4px/py c.x = m/px d.x = 0
8) Suppose a consumer’s utility function is defined by u(x,y)=3x+y for every x≥0 and y≥0 and...
8) Suppose a consumer’s utility function is defined by u(x,y)=3x+y for every x≥0 and y≥0 and the consumer’s initial endowment of wealth is w=100. Graphically depict the income and substitution effects for this consumer if initially Px=1 =Py and then the price of commodity x decreases to Px=1/2.
Utility cobb douglas function = 2X.5Y2 MUx =Y2/X.5 MUy =4X.5Y Px=1 PY=2 and M=100 1.Graph the...
Utility cobb douglas function = 2X.5Y2 MUx =Y2/X.5 MUy =4X.5Y Px=1 PY=2 and M=100 1.Graph the consumer optimization problem in(X,Y) space. Clealy label the precise location of the optimal bundle, the budget constraintm, and the shape of the furthest obtainable indifference curve. 2.Assume Px increase to 2. What is the total effect of the price change in terms of X and Y. 3. What is the precise location of the bundle used to decompose the substitution and income effect? 4.What...
The consumer’s Utility Function is U(x,y) = X1/2Y1/2. Further Px = $5 and Py = $10...
The consumer’s Utility Function is U(x,y) = X1/2Y1/2. Further Px = $5 and Py = $10 and the consumer has $500 to spend. The values of x* = 50 and y* = 25 maximizes utility. The dual to the utility maximization problem is expenditure minimization problem where the consumer choose x and y to minimize the expenditure associated with achieving a specified level of utility. That is, Choose x and y to Minimize Expenditure 5x + 10y subject to U...
Suppose the consumer’s utility function is equal to U=3x+5y. Currently the price of x is $5,...
Suppose the consumer’s utility function is equal to U=3x+5y. Currently the price of x is $5, the price of y is $15 and the income the consumer has to spend on these goods is $100. A) Determine the MRSyx if we consume the bundle of (X,Y) = (1,2). B) What if we consume the bundle of (50,2). C) What is the opportunity cost of X in terms of Y? D) What quantities of X and Y should this consumer consume...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT