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 B and of A. Then derive a formula for Charlie’s marginal rate of substitution of B for A (MRSBA = MUB /MUA ). Calculate the value of his MRS at the bundle (20, 10). Explain what that number means in words. c. Now suppose that Charlie’s weekly income (M) is 40, the price of a banana is PB = 1, and the price of an apple is PA =2. Find a formula for Charlie’s budget constraint, and sketch it on your diagram from part (a). d. Is Charlie’s bundle (20, 10) optimal, given his utility and budget? Explain, both mathematically and referring to your diagram.
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1. Charlie’s utility function for weekly consumption of bananas
(B) and Apples (A) is given by...
Charlie’s utility function is U(xA, xB) = xAxB. Suppose that the price of apples is 1,...
Charlie’s utility function is U(xA, xB) = xAxB. Suppose that the price of apples is 1, the price of bananas is 2, and Charlie’s income is 40. (a) On a graph, use blue ink to draw Charlie’s budget line. (Use a ruler and try to make this line accurate.) Plot a few points on the indifference curve that gives Charlie a utility of 150 and sketch this curve with red ink. Now plot a few points on the indifference curve...
6. A Wisconsin resident Sarah only consumes two goods: Bananas (B) and Apples (A). Her utility...
6. A Wisconsin resident Sarah only consumes two goods: Bananas (B) and Apples (A). Her utility is given by the formula: U AB You are also told that Sarah's marginal utility for consuming bananas and her marginal utility from consuming applies are given by the following equations: Marginal Utility for Bananas: MUB A Marginal Utility for Apples: MUA B a) Given this information and holding everything else constant, fill out all the missing information in the table below. Utility 100...
Dafna’s utility function for weekly consumption of apples (X) and bananas (Y) is given by U...
Dafna’s utility function for weekly consumption of apples (X) and bananas (Y) is given by U = 3XY. a. Derive equations for Dafna’s demand functions for X and Y. b. Draw a diagram of Dafna’s demand curve for apples (X) when PY = 2.5 and M = 100. c. Dafna always spends the same fraction of her budget on apples, no matter what the prices. What fraction is that? Explain. (Hint: Use the demand functions from part a.)
Charlie's utility function for his consumption of apples xA and bananas xB is u(xA, xB) =...
Charlie's utility function for his consumption of apples xA and bananas xB is u(xA, xB) = xAxB. If the price of apples is pA = 3 and the price of bananas is pB = 1, and Charlie has $12 to spend on apples and/or bananas, then: The budget equation is 3 x A + x B = 12 And the optimization condition (to maximize Charlie's utility) is − x B x A = 3 Given these two conditions, find Charlie's...
Can't use Lagrange on this. Multiple Choice Practice- Show work or provide short explanation 4. Charlie's utility function for apples (A) and bananas (B) is U(AB)-AB. The price of apples used...
Can't use Lagrange on this.
Multiple Choice Practice- Show work or provide short explanation 4. Charlie's utility function for apples (A) and bananas (B) is U(AB)-AB. The price of apples used to be S1 per apple and the price of bananas used to be $2 per banana. His incomse was $40 per day. If the price of apples increases to $2.25 and the price of bananas falls to S1.25, then in order to be able to afford his old bundle,...
Charlie’s utility function is ?(??, ??) = ????. The price of apples used to be $1,...
Charlie’s utility function is ?(??, ??) = ????. The price of apples used to be $1, the price of bananas used to be $2, and his income used to be $40. If the price of apples increased to $5 and the price of bananas stayed constant, the substitution effect (not total effect) on Charlie’s apple consumption would reduce his consumption by (choose the closest answer) Answer is 11 apples
4. Charlie likes both apples and bananas. He consumes nothing else. Charlie consumes x bushels of apples per year...
4. Charlie likes both apples and bananas. He consumes nothing else. Charlie consumes x bushels of apples per year and x bushels of bananas per year. Suppose that Charlie's preference is represented in the following utility function: u(x,,Xy)-x,Xy . Suppose that the price of apples is S1, the price of bananas is S2, and Charlie's income is $40. (14 points) a. Draw Charlie's budget line. Plot a few points on the indifference curve that gives Charlie a utility of 150...
The weekly utility function of a consumer is: U = 2AB where A and B are...
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...
3. Consider Charlie who consumes apples (xi) and bananas (2). Suppose that he consumes one apple...
3. Consider Charlie who consumes apples (xi) and bananas (2). Suppose that he consumes one apple and 8 bananas. That is, his current consumption bundle is (1,8). (a) Suppose that Charlie's marginal rate of substitution for one more apple is 2 bananas. If he is offered to trade apples and bananas at one-to-one rate, does he trade? Explain your answer. (b) Suppose that Charlie's preference is convex. If he were to consume 8 apples and one banana, his marginal rate...
Suppose Mike's utility function for apples and bananas is U(A, B) = AB. What is the...
Suppose Mike's utility function for apples and bananas is U(A, B) = AB. What is the marginal utility of apples?* Your answer What is the marginal utility of bananas?* Your answer What is the marginal rate of substitution for apples with 2 bananas? * Your answer
6. A Wisconsin resident Sarah only consumes two goods: Bananas (B) and Apples (A). Her utility is given by the formula: U AB You are also told that Sarah's marginal utility for consuming bananas and her marginal utility from consuming applies are given by the following equations: Marginal Utility for Bananas: MUB A Marginal Utility for Apples: MUA B a) Given this information and holding everything else constant, fill out all the missing information in the table below. Utility 100...
Can't use Lagrange on this.
Multiple Choice Practice- Show work or provide short explanation 4. Charlie's utility function for apples (A) and bananas (B) is U(AB)-AB. The price of apples used to be S1 per apple and the price of bananas used to be $2 per banana. His incomse was $40 per day. If the price of apples increases to $2.25 and the price of bananas falls to S1.25, then in order to be able to afford his old bundle,...
4. Charlie likes both apples and bananas. He consumes nothing else. Charlie consumes x bushels of apples per year and x bushels of bananas per year. Suppose that Charlie's preference is represented in the following utility function: u(x,,Xy)-x,Xy . Suppose that the price of apples is S1, the price of bananas is S2, and Charlie's income is $40. (14 points) a. Draw Charlie's budget line. Plot a few points on the indifference curve that gives Charlie a utility of 150...
3. Consider Charlie who consumes apples (xi) and bananas (2). Suppose that he consumes one apple and 8 bananas. That is, his current consumption bundle is (1,8). (a) Suppose that Charlie's marginal rate of substitution for one more apple is 2 bananas. If he is offered to trade apples and bananas at one-to-one rate, does he trade? Explain your answer. (b) Suppose that Charlie's preference is convex. If he were to consume 8 apples and one banana, his marginal rate...
Suppose Mike's utility function for apples and bananas is U(A, B) = AB. What is the marginal utility of apples?* Your answer What is the marginal utility of bananas?* Your answer What is the marginal rate of substitution for apples with 2 bananas? * Your answer
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