HomeworkLib
Question

The weekly utility function of a consumer is:       U = 2AB where A and B are...

  1. The weekly utility function of a consumer is:       U = 2AB

where A and B are two goods in the consumer’s consumption bundle. Based on this utility function the marginal utility of good A is:

MUA = 2B

and the marginal utility of good B is:

MUB = 2A,

where A and B represent the quantities of good A and good B, respectively. The price of good A is $5 whereas the price good B is $10.

a. Write the utility maximizing condition of this consumer with respect to these two goods.

b. Now suppose that the consumer’s weekly income (budget) is $200. Write the equation for the consumer’s budget line.

c. Carefully plot the budget line. (Put A on the vertical axis and B on the horizontal axis)

d. Determine the utility maximizing combination of A and B for this consumer.

e. Determine the utility the consumer derives from the utility maximizing mix of A and B

f. Draw a (hypothetical) indifference curve reflecting the utility of the consumer consuming the optimal mix of A and B subject to her income constraint.

g. Now suppose the consumer’s income has doubled (to $400). How does this change affect the consumer’s consumption mix and her utility? Show this change on your diagram.

business   economics   
0 0
Add a comment Improve this question Transcribed image text
Next > < Previous
Sort answers by oldest

Homework Answers

Answer #1

0 0
Add a comment
Know the answer?
Add Answer to:
The weekly utility function of a consumer is:       U = 2AB where A and B are...
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. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions

  • 1. Charlie’s utility function for weekly consumption of bananas (B) and Apples (A) is given by...

    1. Charlie’s utility function for weekly consumption of bananas (B) and Apples (A) is given by U = BA . a. Suppose Charlie consumes 20 bananas and 10 apples in a week. Sketch his indifference curve through that bundle on a diagram. (While it doesn’t really matter which good is on the horizontal axis, for consistency with our classwork, assume bananas are on the horizontal axis.) b. Use calculus (partial derivatives) to derive formulas for the marginal utilities (MU) of...

  • Consider a consumer whose utility function is given by U(x, y) = x^1/4y^1/2, where x and...

    Consider a consumer whose utility function is given by U(x, y) = x^1/4y^1/2, where x and y represent quantities of consumption of two consumer goods. (a) Derive and interpret the consumer’s Marshallian demand functions for x and y. (b) Derive and interpret the consumer’s Indirect Utility Function. (c) If the consumer’s income is $1000 and the prices of x and y are both $5, how should the consumer maximize her utility? What is her maximum level of utility? (d) Suppose...

  • 11. If a consumer makes utility-maximizing consumption decision between banana and apple, which of the following...

    11. If a consumer makes utility-maximizing consumption decision between banana and apple, which of the following statement is FALSE? a. MUA * AA = -MUB * AB b. MUA - MUB - РА - Pв c. MRSAR = PA/P d. MRSAR = -AA/AB

  • 1.Suppose a consumer had a utility function given by: U= 9X + 2Y. If the price...

    1.Suppose a consumer had a utility function given by: U= 9X + 2Y. If the price of Good X (Px) is $8 and the price of Good Y is $4then what is the utility maximizing quantity of Good X the consumer will purchase with a budget of $32? 2. Suppose an individual had a utility function given by: U=X^4Y^0.6 Calculate this individual's Marginal Rate of Substitution (MRSxy) when they have a bundle with 3 units of Good X and 1.8...

  • Suppose that Ken cares only about bathing suits (B) and flip-flops (F). His utility function is...

    Suppose that Ken cares only about bathing suits (B) and flip-flops (F). His utility function is U = B 0.6F 0.4. The price of bathing suits are $10, and the price of flip-flops are $4. Ken has a budget of $100. a)Draw a graph containing Ken’s budget line with bathing suits (B) on the x-axis and flip-flops (F) on the y-axis. Define the slope of this line. b)Define the two conditions that need to be met for a consumption allocation...

  • (20 points) Suppose the government wishes to tax a utility maximizing consumer to obtain a certain...

    (20 points) Suppose the government wishes to tax a utility maximizing consumer to obtain a certain amount of tax revenue. A utility maximizing consumer has utility function ?(?, ?) = √? + ?. The price of ? is $1, the price of ? is $4 and the consumer’s income is $120. (a) Suppose the government imposes sales tax ? = 1 on good ? per unit. What is the optimal consumption for good ? and good ? for the consumer...

  • Consider a consumer whose utility function is given by U(x, y) = x^1/3 y^2/3, where x...

    Consider a consumer whose utility function is given by U(x, y) = x^1/3 y^2/3, where x and y represent quantities of consumption of two consumer goods. (a) If the consumer’s income is $100 and the prices of x and y are both $1, how should the consumer maximize her utility? What is her maximum level of utility? (b) If the price of y rose to $2, what would be the resulting income and substitution effects? Illustrate your answer.

  • 1. Dorothy's utility function is U(B, O) = (B + 2) (0 + 1) where B...

    1. Dorothy's utility function is U(B, O) = (B + 2) (0 + 1) where B is her consumption of bananas and O is her consumption of oatmeal. MUB = 0 + 1, MUo = B + 2. (Place Oatmeal on the y axis.) a. Write down the expression and draw Dorothy's indifference curve through (2,8). b. Suppose po = Pb = $1 and M = $11, draw the budget constraint on the same graph as her indifference curve. c....

  • Aaron consumes only 2 goods: avocados (a) and bread (b). His utility function is U(a,b)=ab, with...

    Aaron consumes only 2 goods: avocados (a) and bread (b). His utility function is U(a,b)=ab, with MUa=b and MUb=a. The price of avocados is $4 and Aaron’s income is $24. He spends his entire income on his current consumption bundle of two avocados and eight loaves of bread. a) What is the price of a loaf of bread?

  • A consumer has the utility function U(X, Y) = (X + 2)(Y + 4).  Her income is...

    A consumer has the utility function U(X, Y) = (X + 2)(Y + 4).  Her income is $100, the price of X is $4, and the price of Y is $5. In order to maximize utility subject to her budget constraint, how many units of X and Y will our consumer choose to purchase? Sketch a budget line – indifference curve diagram illustrating this optimum.  Label this optimum A. Suppose the price of X increases to $8, while income and the price...

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT