Question

A consumer has an income of $120 to buy two goods (X, Y). the price of...

A consumer has an income of $120 to buy two goods (X, Y). the price of X is $2 and the price of Y is $4. The consumer utility function is given by ?(?, ?) = ? 2/3 ∗ ? 1/3 You are also told that his marginal utilities are ??? = 2 3 ( ? ? ) 1/3 ??? = 1 3 ( ? ? ) 2/3

1. Find the slope of the budget constrain. (1 point)

2. Calculate the optimal quantity of good X and Y for this consumer (Point A). (2 points)

Assume that the price of good X increases to ?? ′ = $8, and holding everything else constant:

3. Graph all your findings by showing the change in price if good X along the points A and B. (2 points)

Hint: Do not compute and graph point C. Research studies found the demand for good X as follow: ? = 8 −0.4 ∗ ?? + 0.2 ∗ ?? +0.05 ∗ ? where, ?? is the price of good X, ?? is the price of good Y, and M is consumer’s income.

4. Based on this research finding and holding everything else constant, can the consumer afford to buy 12 units of good X. Explain. (2 points)

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
A consumer has preferences represented by the utility function u(x, y) = x^(1/2)*y^(1/2). (This means that...
A consumer has preferences represented by the utility function u(x, y) = x^(1/2)*y^(1/2). (This means that MUx=(1/2)x^(−1/2)*y^(1/2) and MUy =1/2x^(1/2)*y^(−1/2) a. What is the marginal rate of substitution? b. Suppose that the price of good x is 2, and the price of good y is 1. The consumer’s income is 20. What is the optimal quantity of x and y the consumer will choose? c. Suppose the price of good x decreases to 1. The price of good y and...
Suppose there are two goods, X and Y.  The price of good X is $2 per unit...
Suppose there are two goods, X and Y.  The price of good X is $2 per unit and the price of good Y is $3 per unit.  A given consumer with an income of $300 has the following utility function: U(X,Y) = X0.8Y0.2         which yields marginal utilities of: MUX= 0.8X-0.2Y0.2 MUY= 0.2X0.8Y-0.8         a.     What is the equation for this consumer’s budget constraint in terms of X and Y?         b.    What is the equation for this consumer’s marginal rate of substitution (MRSXY)?  Simplifyso you only have...
Consider a consumer with Cobb-Douglas preferences over two goods, x and y described by the utility...
Consider a consumer with Cobb-Douglas preferences over two goods, x and y described by the utility function u(x, y) = 1/3ln(x) + 2/3n(y) 1. Assume the prices of the two goods are initially both $10, and her income is $1000. Obtain the consumer’s demands for x and y. 2. If the price of good x increases to $20, what is the impact on her demand for good x? 3. Decompose this change into the substitution effect, and the income effect....
A basket of goods for a given consumer includes two​ goods, X and Z. Consumer income...
A basket of goods for a given consumer includes two​ goods, X and Z. Consumer income is equal to ​$1,500 and the prices of these two goods are as​ follows: Px​ = ​$25 Pz​ = ​$50 This consumer is consuming 10 units of good X. Suppose that over the course of a​ year, the price of good X changes by −10​% and the price of good Z changes by 10​%. How much income would be required for the consumer to...
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...
1. A consumer has the utility function U = min(2X, 5Y ). The budget constraint isPXX+PYY...
1. A consumer has the utility function U = min(2X, 5Y ). The budget constraint isPXX+PYY =I. (a) Given the consumer’s utility function, how does the consumer view these two goods? In other words, are they perfect substitutes, perfect complements, or are somewhat substitutable? (2 points) (b) Solve for the consumer’s demand functions, X∗ and Y ∗. (5 points) (c) Assume PX = 3, PY = 2, and I = 200. What is the consumer’s optimal bundle? (2 points) 2....
Consider the budget set for a consumer with income of 100 facing the following prices. The...
Consider the budget set for a consumer with income of 100 facing the following prices. The price for the first five units of good 1 is $10 (per unit) If the consumer buys more than five units, the price is $5 for any subsequent unit purchased. If the consumer spends all of her money on good 1, how many units of good 1 can she buy? 10 12 15 20 25 Well-behaved preferences are convex monotonic reach the consumer’s bliss...
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...
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 $4. How much would they buy now?    c. Decompose the total effect of the price change on demand for x into the substitution effect and the...
Suppose that a consumer has a 10$ budget. The price of Good X is $2 and...
Suppose that a consumer has a 10$ budget. The price of Good X is $2 and the price of Good Y is $1. Which of the following bundles would the consumer be able to purchase with a voucher for Good X of $8 (The consumer may still have some of the cash or voucher left unused) a. X = 3. Y= 10 b. X = 5. Y= 10 c. X = 1. Y= 14 d. X = 6. Y= 6...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT