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4. A person with the utility function U(x,y)= 10 +y2...
Problem 1 (10pts) Jim's utility function is U (x, y) = xy. Jerry's utility function is...
Problem 1 (10pts) Jim's utility function is U (x, y) = xy. Jerry's utility function is U (x,y) = 1,000xy +2,000. Tammy's utility function is U2, y) = xy(1 - xy). Bob's utility function is U(x,y) = -1/(10+ 2xy). Mark's utility function is U (2,y) = x(y + 1,000). Pat's utility function is U (2,y) = 0.5cy - 10,000. Billy's utility function is U (x,y) = x/y. Francis' utility function is U (x,y) = -ry. a. Who has the same...
3. Suppose the utility function for two goods, x and y, is: U = U(x,y) =...
3. Suppose the utility function for two goods, x and y, is: U = U(x,y) = xłyż. a. Graph the indifference curve for U = 10. b. If x = 5, what must y equal to be on the U = 10 indifference curve? What is the MRS at this point? c. Derive a general expression for the MRS for this utility function. Show how it can be interpreted as the ratio of the marginal utilities. d. Does this individual...
5. A person has utility function u(x, y) = 100xy + x + 2y. Suppose that...
5. A person has utility function u(x, y) = 100xy + x + 2y. Suppose that the price per unit of x is $2, and that the price per unit of y is $4. The person receives $1 000 that all has to be spent on the two commodities x and y. Solve the utility maximization problem.
5. Consider the utility function U(x, y) = 2/x + y. 1) Is the assumption that...
5. Consider the utility function U(x, y) = 2/x + y. 1) Is the assumption that "more is better” satisfied for both goods? 2) What is MRS, for this utility function? 3) Is the marginal rate of substitution diminishing, constant, or increasing in x as the consumer substitutes x for y along an indifference curve? 4) Will the indifference curve corresponding to this utility function be convex to the origin, concave to the origin, or straight lines? Explain.
3. A consumer's preferences over a and y are given by the utility function u(x,y) -...
3. A consumer's preferences over a and y are given by the utility function u(x,y) - 2vr 2/y. The individual's income is I $100. The price of a unit of good c is $2, while the price of a unit of good y is S1. a) Graphically describe: i. the consumer's preferences for r and y ii. the budget constraint (b) Find the optimal x that the consumer would choose. You may assume (c) What is the consumer's MRS at...
Joe has a utility function given by u(x, y) = x^ 2 + 2xy + y^...
Joe has a utility function given by u(x, y) = x^ 2 + 2xy + y^ 2 a. Compute Joes marginal rate of substitution, MRS(x, y). b. Joe’s cousin, Alex, has a utility function v(x, y) = x+y. Compute Alex’s marginal rate of substitution, MRS(x, y). c. Do u(x, y) and v(x, y) represent the same preferences?
For U(x,y) -xy, MRS ▼ , while Uxx_ and Uyy This means that this utility function...
For U(x,y) -xy, MRS ▼ , while Uxx_ and Uyy This means that this utility function has MRS, while exhibiting marginal utility in x andy For U(x,y)-x2y2, MRS ▼ , while Uxx_ and Uyy This means that this utility function has MRS, while exhibiting marginal utility in x and y For U(x,y) = In x + In y, MRS- ,while Ux- and Uyy ▼ . This means that this utility function has MRS, while exhibiting marginal utility in x and...
Problem 1 (10 marks) Answer the following questions regarding a Cobb-Douglas utility function U(X,Y)= X0.3 0.7...
Problem 1 (10 marks) Answer the following questions regarding a Cobb-Douglas utility function U(X,Y)= X0.3 0.7 (a) Does this utility function exhibit diminishing marginal utility in X? Show why or why not. (b) Does this utility function exhibit diminishing marginal rate of substitution? Mathematically show and verbally explain why it has (or doesn't have) such property. Problem 2 (10 marks) Consider the following utility function U(X,Y)= X14734 Suppose that prices and income are given as following Px= 1 Py =...
Suppose a consumer's preferences can be represented by the utility function: U(X,Y)=X3/5Y1/4 a. Derive the function...
Suppose a consumer's preferences can be represented by the utility function: U(X,Y)=X3/5Y1/4 a. Derive the function for the marginal rate of substitution holding utility constant: U X Y b. Derive the demand curves for the two goods, X and Y. c. Confirm that both demand curves slope downward. d. Calculate the price elasticity for each of the goods. e. Calculate the income elasticity for each of the goods.
ots) Mark has preferences that can be represented by the following utility function: U(x,y)= (18+x)(+1). Sarah's...
ots) Mark has preferences that can be represented by the following utility function: U(x,y)= (18+x)(+1). Sarah's utility function is v) 6x +60 y - 4x + 2xy - 24 y +29: Do Mark and Sarah have the same preferences? You must prove your answer. U (x, y) = 6x+60 y - 4x + 2
Problem 1 (10pts) Jim's utility function is U (x, y) = xy. Jerry's utility function is U (x,y) = 1,000xy +2,000. Tammy's utility function is U2, y) = xy(1 - xy). Bob's utility function is U(x,y) = -1/(10+ 2xy). Mark's utility function is U (2,y) = x(y + 1,000). Pat's utility function is U (2,y) = 0.5cy - 10,000. Billy's utility function is U (x,y) = x/y. Francis' utility function is U (x,y) = -ry. a. Who has the same...
3. Suppose the utility function for two goods, x and y, is: U = U(x,y) = xłyż. a. Graph the indifference curve for U = 10. b. If x = 5, what must y equal to be on the U = 10 indifference curve? What is the MRS at this point? c. Derive a general expression for the MRS for this utility function. Show how it can be interpreted as the ratio of the marginal utilities. d. Does this individual...
5. A person has utility function u(x, y) = 100xy + x + 2y. Suppose that the price per unit of x is $2, and that the price per unit of y is $4. The person receives $1 000 that all has to be spent on the two commodities x and y. Solve the utility maximization problem.
5. Consider the utility function U(x, y) = 2/x + y. 1) Is the assumption that "more is better” satisfied for both goods? 2) What is MRS, for this utility function? 3) Is the marginal rate of substitution diminishing, constant, or increasing in x as the consumer substitutes x for y along an indifference curve? 4) Will the indifference curve corresponding to this utility function be convex to the origin, concave to the origin, or straight lines? Explain.
3. A consumer's preferences over a and y are given by the utility function u(x,y) - 2vr 2/y. The individual's income is I $100. The price of a unit of good c is $2, while the price of a unit of good y is S1. a) Graphically describe: i. the consumer's preferences for r and y ii. the budget constraint (b) Find the optimal x that the consumer would choose. You may assume (c) What is the consumer's MRS at...
For U(x,y) -xy, MRS ▼ , while Uxx_ and Uyy This means that this utility function has MRS, while exhibiting marginal utility in x andy For U(x,y)-x2y2, MRS ▼ , while Uxx_ and Uyy This means that this utility function has MRS, while exhibiting marginal utility in x and y For U(x,y) = In x + In y, MRS- ,while Ux- and Uyy ▼ . This means that this utility function has MRS, while exhibiting marginal utility in x and...
Problem 1 (10 marks) Answer the following questions regarding a Cobb-Douglas utility function U(X,Y)= X0.3 0.7 (a) Does this utility function exhibit diminishing marginal utility in X? Show why or why not. (b) Does this utility function exhibit diminishing marginal rate of substitution? Mathematically show and verbally explain why it has (or doesn't have) such property. Problem 2 (10 marks) Consider the following utility function U(X,Y)= X14734 Suppose that prices and income are given as following Px= 1 Py =...
ots) Mark has preferences that can be represented by the following utility function: U(x,y)= (18+x)(+1). Sarah's utility function is v) 6x +60 y - 4x + 2xy - 24 y +29: Do Mark and Sarah have the same preferences? You must prove your answer. U (x, y) = 6x+60 y - 4x + 2
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