Homework Answers
1.
Marginal utility of apples = MUa
MUa = d(A^2B)/dA
MUa = B*2A + A^2*0
MUa = 2AB
B.
Marginal utility of bananas = MUb
MUb = d(A^2B)/db
MUb = A^2 + B*0
MUb = A^2
C.
Marginal rate of substitution= MRSab
MRSab = MUa/MUb = 2AB/A^2
MRSab = 2B/A
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Suppose Mike's utility function for apples and bananas is U(A, B) = AB. What is the...
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 consumes apples and bananas. His utility function is: U(xA; xB) xAxB. The price of apples...
Charlie consumes apples and bananas. His utility function is: U(xA; xB) xAxB. The price of apples is $1, the price of bananas is $2, and Charlie's income is $40 a day. The price of bananas suddenly falls to $1. Find the substitution and income effect of the price change for apples and bananas.
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...
If the utility function (U) between bananas (B) and jam (J) can be represented as U(B,J)...
If the utility function (U) between bananas (B) and jam (J) can be represented as U(B,J) = 3ln(B)+4ln(J), what is the marginal rate of substitution (MRSBJ) between bananas and jam? I know the answer I am just trying to figure out how to get there..
3. Suppose your utility function (e. level of satisfaction from consuming a and b) is given...
3. Suppose your utility function (e. level of satisfaction from consuming a and b) is given by U(a, b)=a 1/32/3 where a represents apple and b represents banana. Your total income is $500. The price of apple is $5 and the price of banana is $10. (a) Write your Budget Constraint (BC). What is the Marginal Rate of Transformation? (b) Find the Marginal Rate of Substitution. (c) Find the consumption combination of bananas and apples that maximizes your utility given...
3. Suppose a consumer's utility function is given by U(A, B) In(A)+In(B). Suppose the price of...
3. Suppose a consumer's utility function is given by U(A, B) In(A)+In(B). Suppose the price of each apple (A) is €6, and the price of a loaf of bread (B) Is €6 and the consumer's income is €120 ) Write down the Lagrangian for this problem and solve for the optimal consumption of apples and (ii) Report and interpret your solution for the Lagrange multiplier. bread. i) Evaluate the marginal utility of bread and the marginal utility of apples at...
Diana's utility function for consuming apples (Xa) and Bananas (Xb) is U(Xa,Xb) = XaXb. Suppose the...
Diana's utility function for consuming apples (Xa) and Bananas (Xb) is U(Xa,Xb) = XaXb. Suppose the prices of apples is $1, bananas $2, and her income is $40. On a graph with bananas on the y-axis, use blue ink to draw Bianca’s budget line.With red ink, plot an indifference curve that gives her a utility level of 150. Using black ink, plot an indifference curve that gives her a utility level of 300. Can Bianca afford any bundles that give...
2. Mike's preferences are represented by the utility function U(A, B) A+2B. He has an income...
2. Mike's preferences are represented by the utility function U(A, B) A+2B. He has an income of $20. Consider each of the following combination of prices of goods. On the same graph, (i) graph a family of indifference curves for the consumer, (ü) graph the budget lines for each combination of prices, (i cakculate and label the optimal consumption choice(s) for each combination of prices, and (iv) cakulate the utility Mike derives from consuming the optimal consumption choice. bananas 20...
2. Mike's preferences are represented by the utility function U(A, B) A+2B. He has an income...
2. Mike's preferences are represented by the utility function U(A, B) A+2B. He has an income of S20. Consider each of the following combination of prices of goods. On the same graph, (i) graph a family of indifference curves for the consumer, (ii) graph the budget lines for each combination of prices, (iii) calculate and label the optimal consumption choice(s) for each combination of prices, and (iv) calculate the utility Mike derives from consuming the optimal consumption choice. bananas 20...
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...
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 consumes apples and bananas. His utility function is: U(xA; xB) xAxB. The price of apples is $1, the price of bananas is $2, and Charlie's income is $40 a day. The price of bananas suddenly falls to $1. Find the substitution and income effect of the price change for apples and bananas.
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...
3. Suppose your utility function (e. level of satisfaction from consuming a and b) is given by U(a, b)=a 1/32/3 where a represents apple and b represents banana. Your total income is $500. The price of apple is $5 and the price of banana is $10. (a) Write your Budget Constraint (BC). What is the Marginal Rate of Transformation? (b) Find the Marginal Rate of Substitution. (c) Find the consumption combination of bananas and apples that maximizes your utility given...
3. Suppose a consumer's utility function is given by U(A, B) In(A)+In(B). Suppose the price of each apple (A) is €6, and the price of a loaf of bread (B) Is €6 and the consumer's income is €120 ) Write down the Lagrangian for this problem and solve for the optimal consumption of apples and (ii) Report and interpret your solution for the Lagrange multiplier. bread. i) Evaluate the marginal utility of bread and the marginal utility of apples at...
2. Mike's preferences are represented by the utility function U(A, B) A+2B. He has an income of $20. Consider each of the following combination of prices of goods. On the same graph, (i) graph a family of indifference curves for the consumer, (ü) graph the budget lines for each combination of prices, (i cakculate and label the optimal consumption choice(s) for each combination of prices, and (iv) cakulate the utility Mike derives from consuming the optimal consumption choice. bananas 20...
2. Mike's preferences are represented by the utility function U(A, B) A+2B. He has an income of S20. Consider each of the following combination of prices of goods. On the same graph, (i) graph a family of indifference curves for the consumer, (ii) graph the budget lines for each combination of prices, (iii) calculate and label the optimal consumption choice(s) for each combination of prices, and (iv) calculate the utility Mike derives from consuming the optimal consumption choice. bananas 20...
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...
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