Question

There are two goods, Good 1 and Good 2, with positive prices p1 and p2. A...

There are two goods, Good 1 and Good 2, with positive prices p1 and p2. A consumer has the utility function U(x1, x2) = min{2x1, 5x2}, where “min” is the minimum function, and x1 and x2 are the amounts she consumes of Good 1 and Good 2. Her income is M > 0.

(a) What condition must be true of x1 and x2, in any utility-maximising bundle the consumer chooses? Your answer should be an equation involving (at least) these two variables.

(b) Use the answer to (a), along with the budget constraint, to calculate the consumer’s demand functions for both goods.

(c) Is Good 2 a normal good? Explain your answer.

(d) Are the goods complements, substitutes, or neither? Explain your answer.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
There are two goods, Good 1 and Good 2, with positive prices p1 and p2. A...
There are two goods, Good 1 and Good 2, with positive prices p1 and p2. A consumer has the utility function U(x1, x2) = min{2x1, 5x2}, where “min” is the minimum function, and x1 and x2 are the amounts she consumes of Good 1 and Good 2. Her income is M > 0. (a) What condition must be true of x1 and x2, in any utility-maximising bundle the consumer chooses? Your answer should be an equation involving (at least) these...
2. A consumer has the utility function U ( X1, X2 ) = X1 + X2...
2. A consumer has the utility function U ( X1, X2 ) = X1 + X2 + X1X2 and the budget constraint P1X1 + P2X2 = M , where M is income, and P1 and P2 are the prices of the two goods. . a. Find the consumer’s marginal rate of substitution (MRS) between the two goods. b. Use the condition (MRS = price ratio) and the budget constraint to find the demand functions for the two goods. c. Are...
1. Consider a utility-maximizing price-taking consumer in a two good world. Denote her budget constraint by...
1. Consider a utility-maximizing price-taking consumer in a two good world. Denote her budget constraint by p1x1 + p2x2 = w, p1, p2, w > 0, x1, x2 ≥ 0 (1) and suppose her utility function is u (x1, x2) = 2x 1/2 1 + x2. (2) Since her budget set is compact and her utility function is continuous, the Extreme Value Theorem tells us there is at least one solution to this optimization problem. In fact, demand functions, xi(p1,...
Suppose you consume two goods, whose prices are given by p1 and p2, and your income...
Suppose you consume two goods, whose prices are given by p1 and p2, and your income is m. Solve for your demand functions for the two goods, if (a) your utility function is given by U(x1, x2) = ax1 + bx2 (b) your utility function is given by U(x1, x2) = max{ax1, bx2}
Suppose that a consumer has preferences over bundles of non-negative amounts of each two goods, x1...
Suppose that a consumer has preferences over bundles of non-negative amounts of each two goods, x1 and x2, that can be represented by a quasi-linear utility function of the form U(x1,x2)=x1 +√x2. The consumer is a price taker who faces a price per unit of good one that is equal to $p1 and a price per unit of good two that is equal to $p2. An- swer each of the following questions. To keep things relatively simple, focus only on...
Each individual consumer takes the prices as given and chooses her consumption bundle,(x1,x2)ER^2, by maximizing the...
Each individual consumer takes the prices as given and chooses her consumption bundle,(x1,x2)ER^2, by maximizing the utility function: U(x1,x2) = ln(x1^3,x2^3), subject to the budget constraint p1*x1+p2*x2 = 1000 a) write out the Lagrangian function for the consumer's problem b) write out the system of first-order conditions for the consumer's problem c) solve the system of first-order conditions to find the optimal values of x1, x2. your answer might depend on p1 and p2. d) check if the critical point...
Consider the problem of a consumer who must choose between two types of goods, good 1...
Consider the problem of a consumer who must choose between two types of goods, good 1 (x1) and good 2 (x2) costing respectively p1 and p2 per unit. He is endowed with an income m and has a quasi-concave utility function u defined by u(x1, x2) = 5 ln x1 + 3 ln x2. 1. Write down the problem of the consumer. 1 mark 2. Determine the optimal choice of good 1 and good 2, x ∗ 1 = x1(p1,...
Bilbo can consume two goods, good 1 and good 2 where X1 and X2 denote the...
Bilbo can consume two goods, good 1 and good 2 where X1 and X2 denote the quantity consumed of each good. These goods sell at prices P1 and P2, respectively. Bilbo’s preferences are represented by the following utility function: U(X1, X2) = 3x1X2. Bilbo has an income of m. a) Derive Bilbo’s Marshallian demand functions for the two goods. b) Given your answer in a), are the two goods normal goods? Explain why and show this mathematically. c) Calculate Bilbo’s...
Given a utility function for perfect complements: U(x1,x2) = min{x1,βx2}, where β is a positive num-...
Given a utility function for perfect complements: U(x1,x2) = min{x1,βx2}, where β is a positive num- ber, and a budget constraint: p1x1 + p2x2 = Y , where p1 and p2 are prices of good 1 and good 2 respectively, Y is the budget for the complements. Find the demand functions for good 1 and good 2.
Suppose x1 and x2 are perfect substitutes with the utility function U(x1, x2) = 2x1 +...
Suppose x1 and x2 are perfect substitutes with the utility function U(x1, x2) = 2x1 + 6x2. If p1 = 1, p2 = 2, and income m = 10, what it the optimal bundle (x1*, x2*)?