Homework Answers
3. True
Reason: This is because as utility increases, cost to the consumer increases. And an increase in cost is associated positively with the price of X. That is, as price of X increases, cost to the consumer increases as he is sending more money to buy it and is not substituting it. This means X is a normal good as its demand is positively related to its price.
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-1, the Marshallian elasticity of Y with respect to Px must be equal to O at that optimum. 3. (5 ...
A consumer has the utility function over goods X and Y, U(X; Y) = X1/3Y1/2 Let...
A consumer has the utility function over goods X and Y, U(X; Y) = X1/3Y1/2 Let the price of good x be given by Px, let the price of good y be given by Py, and let income be given by I. Derive the consumer’s generalized demand function for good X. Solve for the Marshallian Demand for X and Y using Px, and Py (there are no numbers—use the notation). c. Is good Y normal or inferior? Explain precisely.
Consider a consumer whose income is 100 and his preference is given by U-10x04yo6. If PX-Py-1,...
Consider a consumer whose income is 100 and his preference is given by U-10x04yo6. If PX-Py-1, what is the optimal consumption bundle by the consumer? (Please write out the constraint utility maximization problem completely, including the budget function.) Derive the demand of Good X and Y by this consumer. (The result should be a function giving you the amount of X he will buy at every given price level Px, and a function for good Y as well.) a. b....
1 Elasticity This problem continues on from the previous homework. Consider the market for good X....
1 Elasticity This problem continues on from the previous homework. Consider the market for good X. The demand function is and the supply function is Px, Py, and Pz are the prices of goods X, Y, and Z. M is the average consumer income Suppose market research determines that M 105, Py 20, and Pz 10. 1.a Caleulate the cross-price clasticities of demand with respect to good Y and good Z at the market cquilibrium. Are goods Y and Z...
1. Suppose a consumer has the utility function over goods x and y u(x,y) = 3x{y}...
1. Suppose a consumer has the utility function over goods x and y u(x,y) = 3x{y} (a) Setup the utility maximization problem for this consumer using the general budget con- straint. (2 points) (b) Will the constraint be active/binding? Is the sufficient condition for interior solution satisfied? Prove your answers. (4 points) (c) Solve the utility maximization problem for the Marshallian demand equations x* (Px. Py,m) and y* (Px.p.m). Show all of your work and circle your final answers. (7...
1. Suppose a consumer has the utility function over goods x and y u(x, y) =...
1. Suppose a consumer has the utility function over goods x and y u(x, y) = 3x}}} (a) Setup the utility maximization problem for this consumer using the general budget con- straint. (2 points) (b) Will the constraint be active/binding? Is the sufficient condition for interior solution satisfied? Prove your answers. (4 points) (c) Solve the utility maximization problem for the Marshallian demand equations x (Px, py,m) and y* (Px, Py,m). Show all of your work and circle your final...
1. Suppose a consumer has the utility function over goods x and y u(x,y) = 3x3...
1. Suppose a consumer has the utility function over goods x and y u(x,y) = 3x3 yž (a) Setup the utility maximization problem for this consumer using the general budget con- straint. (2 points) (b) Will the constraint be active/binding? Is the sufficient condition for interior solution satisfied? Prove your answers. (4 points) (c) Solve the utility maximization problem for the Marshallian demand equations x* (Px, Py,m) and y* (Px, Py,m). Show all of your work and circle your final...
(a) A representative consumer has a utility function U (x, y) = xy. A representative firm makes good x and has a product...
(a) A representative consumer has a utility function U (x, y) = xy. A representative firm makes good x and has a production function x = f(k, l) = (kl)0.25and an unavoidable fixed cost equal to A. There are 100 consumers and, initially, 100 firms. Prices are w = v = Py = 1 and Px is determined in a competitive market. Representative consumer income is I = 2. (a) Find the representative individual’s Marshallian demand for good x?
Suppose your utility function is U (x, y) = 2 ln(2) + 4y c) Given PX...
Suppose your utility function is U (x, y) = 2 ln(2) + 4y c) Given PX - 1. Py = 2, and M =5. Find the elasticity of demand (own-price elasticity) for good x -- is good x ordinary or Giffen? Edit View Insert Format Tools Table 12pt Paragraph B I VART :
P X Y = + MRS= 19. Consider a consumer with preferences: u(x,y) = Ý 1...
P X Y = + MRS= 19. Consider a consumer with preferences: u(x,y) = Ý 1 Py + In y. (a) 12 points Derive the Hicksian demands and expenditure function L = Pxx t Py Pe X +Py Ye=m PxX+ Px=m ok: Px - Aco d. Py - X J dy OL:x+ldy) - u zo 1/v/P, P,m) = m-Px + ln o ū= e-Px X (b) 4 points Verify Shephard's Lemma for this consumer. - e-Px ü
1. (34 points) Consider the demand function for good X: x= (A P3 - MP,Px M...
1. (34 points) Consider the demand function for good X: x= (A P3 - MP,Px M = income M= 1 Px = 1 Py = 3 a) (7 points) Calculate the value of own-price elasticity of good X, ε. b) (9 points) Suppose ε = -0.9. Explain what this tells you. c) (7 points) Calculate the value of cross-price elasticity (the elasticity of good X with respect to the price of good Y), Exp... d) (11 points) Suppose Exp, =...
Consider a consumer whose income is 100 and his preference is given by U-10x04yo6. If PX-Py-1, what is the optimal consumption bundle by the consumer? (Please write out the constraint utility maximization problem completely, including the budget function.) Derive the demand of Good X and Y by this consumer. (The result should be a function giving you the amount of X he will buy at every given price level Px, and a function for good Y as well.) a. b....
1 Elasticity This problem continues on from the previous homework. Consider the market for good X. The demand function is and the supply function is Px, Py, and Pz are the prices of goods X, Y, and Z. M is the average consumer income Suppose market research determines that M 105, Py 20, and Pz 10. 1.a Caleulate the cross-price clasticities of demand with respect to good Y and good Z at the market cquilibrium. Are goods Y and Z...
1. Suppose a consumer has the utility function over goods x and y u(x,y) = 3x{y} (a) Setup the utility maximization problem for this consumer using the general budget con- straint. (2 points) (b) Will the constraint be active/binding? Is the sufficient condition for interior solution satisfied? Prove your answers. (4 points) (c) Solve the utility maximization problem for the Marshallian demand equations x* (Px. Py,m) and y* (Px.p.m). Show all of your work and circle your final answers. (7...
1. Suppose a consumer has the utility function over goods x and y u(x, y) = 3x}}} (a) Setup the utility maximization problem for this consumer using the general budget con- straint. (2 points) (b) Will the constraint be active/binding? Is the sufficient condition for interior solution satisfied? Prove your answers. (4 points) (c) Solve the utility maximization problem for the Marshallian demand equations x (Px, py,m) and y* (Px, Py,m). Show all of your work and circle your final...
1. Suppose a consumer has the utility function over goods x and y u(x,y) = 3x3 yž (a) Setup the utility maximization problem for this consumer using the general budget con- straint. (2 points) (b) Will the constraint be active/binding? Is the sufficient condition for interior solution satisfied? Prove your answers. (4 points) (c) Solve the utility maximization problem for the Marshallian demand equations x* (Px, Py,m) and y* (Px, Py,m). Show all of your work and circle your final...
Suppose your utility function is U (x, y) = 2 ln(2) + 4y c) Given PX - 1. Py = 2, and M =5. Find the elasticity of demand (own-price elasticity) for good x -- is good x ordinary or Giffen? Edit View Insert Format Tools Table 12pt Paragraph B I VART :
P X Y = + MRS= 19. Consider a consumer with preferences: u(x,y) = Ý 1 Py + In y. (a) 12 points Derive the Hicksian demands and expenditure function L = Pxx t Py Pe X +Py Ye=m PxX+ Px=m ok: Px - Aco d. Py - X J dy OL:x+ldy) - u zo 1/v/P, P,m) = m-Px + ln o ū= e-Px X (b) 4 points Verify Shephard's Lemma for this consumer. - e-Px ü
1. (34 points) Consider the demand function for good X: x= (A P3 - MP,Px M = income M= 1 Px = 1 Py = 3 a) (7 points) Calculate the value of own-price elasticity of good X, ε. b) (9 points) Suppose ε = -0.9. Explain what this tells you. c) (7 points) Calculate the value of cross-price elasticity (the elasticity of good X with respect to the price of good Y), Exp... d) (11 points) Suppose Exp, =...
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