A consumer has income M, and faces prices (for goods 1 and 2) p1 and p2....
A consumer has income M, and faces prices (for goods 1 and 2) p1
and p2. For each of the following utility functions, graphically
show the following:
(i) the Slutsky substitution and income e⁄ects when p1
decreases.
(ii) the Hicks substitution and income e⁄ects when p1 decreases.
(iii) the Marshallian and Hicksian demand curves for good 1:
(a) perfect complements: U(x1 , x2) = min {4x1, 5x2}
(b) quasi-linear: U(x1 , x2) = x^2/3 1 + x2
Homework Answers
Add Answer to:
A consumer has income M, and faces prices (for goods 1 and 2) p1
and p2....
Suppose that a consumer has a utility function given by u(x1, x2) = 2x1 + x2. Initially the consumer faces prices (2, 2) and has income 24. i. Graph the budget constraint and indifference curves. Find...
Suppose that a consumer has a utility function given by u(x1, x2) = 2x1 + x2. Initially the consumer faces prices (2, 2) and has income 24. i. Graph the budget constraint and indifference curves. Find the initial optimal bundle. ii. If the prices change to (6, 2), find the new optimal bundle. Show this in your graph in (i). iii. How much of the change in demand for x1 is due to the substitution effect? How much due to...
The individual has a utility function of u(x1, x2) = min (4x1, 5x2) and faces prices...
The individual has a utility function of u(x1, x2) = min (4x1, 5x2) and faces prices p1=2 and p2=1. We know they consume 20 units of x2 and spend all their income. What is the demand function for x1?
The utility function is u = x1½ + x2, and the budget constraint is m =...
The utility function is u = x1½ + x2, and the budget constraint is m = p1x1 + p2x2. Derive the optimal demand curve for good 1, x1(p1, p2), and good 2, x2(m, p1, p2). Looking at the cross price effects (∂x1/∂p2 and ∂x2/∂p1) are goods x1 and x2 substitutes or complements? Looking at income effects (∂x1/∂m and ∂x2/∂m) are goods x1 and x2 inferior, normal or neither? Assume m=100, p1=0.5 and p2=1. Using the demand function you derived in...
3. When prices are (p1,P2) (1,2) a consumer demands (xi, 2) (1,2), and when prices are...
3. When prices are (p1,P2) (1,2) a consumer demands (xi, 2) (1,2), and when prices are (p1,P2) (2,1) the consumer demands (x1,x2)-(2,1). Is this behavior consistent with the model of utility maximization?
Suppose an individual’s utility function is u=x11/2, x21/2. Let p1=4, p2=5, and income equal $200. With...
Suppose an individual’s utility function is u=x11/2, x21/2. Let p1=4, p2=5, and income equal $200. With a general equation and general prices, derive the equal marginal principle. Graphically illustrate equilibrium and disequilibrium conditions and how consumers can reallocate their consumption to maximize utility. What is the optimal amount of x1 consumed? What is the optimal amount of x2 consumed? What is the marginal rate of substitution at the optimal amounts of x1 and x2? As functions of p1, p2, and...
Q6 Deriving Demand Function Derive demand functions x1(P1, P2, m) and x2(P1, P2, m) for the...
Q6 Deriving Demand Function Derive demand functions x1(P1, P2, m) and x2(P1, P2, m) for the consumer with the utility function U(x1, x2) = xi x2
A consumer uses his income I for the consumption of two goods ?1 and ?2. He maximises utility at given product prices ?1...
A consumer uses his income I for the consumption of two goods ?1 and ?2. He maximises utility at given product prices ?1, ?2. His preferences with respect to both products can be described by an ordinal utility function ?(?1,?2), which exhibits a decreasing marginal rate of substitution (normal preferences). Please indicate whether the following statements are right or wrong in this context. If a statement is wrong, then describe briefly what is wrong (one sentence). a) A double value...
Given the following utility function: Where, q1 and q2 are consumer goods and the budget constraint...
Given the following utility function:
Where, q1 and q2 are consumer goods and the budget
constraint is given as.
With p, and p the prices of the goods and the month
the income. Find.
1. The Marshallian Demands for (q1 and 92.
2. The Indirect Utility Function, V (p1, p2, m)
3. The Hicksian Demands for q1 and q2.
4. The Expenditure Function, m (p1, p2, U)
U(992)=9, +10 log2 U(992)=9, +10 log2
2. (25%) Consider a consumer with preferences represented by the utility function: u(x1, x2) = min...
2. (25%) Consider a consumer with preferences represented by the utility function: u(x1, x2) = min {axı, bx2} If the income of the consumer is w > 0 and the prices are p1 > 0 and P2 > 0. (a) Derive the Marshallian demands. Be sure to show all your work. (b) Derive the indirect utility function. (c) Does the utility function: û(x1, x2) = axı + bx2 represent the same preferences?
Q2 For each of the following utility functions, derive the consumer's Marshallian demand functions, 21(P1, P2,...
Q2 For each of the following utility functions, derive the consumer's Marshallian demand functions, 21(P1, P2, B) and x (P1, P2, B), and calculate 11 (income elasticity of good 1), €1 (own-price elasticity of good 1), and €12 (cross-price elasticity). a U(x1, x2) = 21 b U(x1, x2) = 2.925-a for a € (0,1) CU(21, 12) = ln(21) + x2 where B > P2.
3. When prices are (p1,P2) (1,2) a consumer demands (xi, 2) (1,2), and when prices are (p1,P2) (2,1) the consumer demands (x1,x2)-(2,1). Is this behavior consistent with the model of utility maximization?
Q6 Deriving Demand Function Derive demand functions x1(P1, P2, m) and x2(P1, P2, m) for the consumer with the utility function U(x1, x2) = xi x2
Given the following utility function:
Where, q1 and q2 are consumer goods and the budget
constraint is given as.
With p, and p the prices of the goods and the month
the income. Find.
1. The Marshallian Demands for (q1 and 92.
2. The Indirect Utility Function, V (p1, p2, m)
3. The Hicksian Demands for q1 and q2.
4. The Expenditure Function, m (p1, p2, U)
U(992)=9, +10 log2 U(992)=9, +10 log2
2. (25%) Consider a consumer with preferences represented by the utility function: u(x1, x2) = min {axı, bx2} If the income of the consumer is w > 0 and the prices are p1 > 0 and P2 > 0. (a) Derive the Marshallian demands. Be sure to show all your work. (b) Derive the indirect utility function. (c) Does the utility function: û(x1, x2) = axı + bx2 represent the same preferences?
Q2 For each of the following utility functions, derive the consumer's Marshallian demand functions, 21(P1, P2, B) and x (P1, P2, B), and calculate 11 (income elasticity of good 1), €1 (own-price elasticity of good 1), and €12 (cross-price elasticity). a U(x1, x2) = 21 b U(x1, x2) = 2.925-a for a € (0,1) CU(21, 12) = ln(21) + x2 where B > P2.
Most questions answered within 3 hours.
-
You have a 825.3 mL sample of 2.754 M HA (Ka =
4.49⋅10−4). Calculate the pH...
asked 35 minutes ago -
The blues made its way into many kinds of music. Eric Clapton,
The Beatles, and Elvis...
asked 2 hours ago -
8. A wave in a string has a wave function given by: y (x, t) =...
asked 1 hour ago -
If you’re standing at the bottom of a hill and asked to evaluate
it while being...
asked 3 hours ago -
1. Which region has taken the lead in the world of
e-waste handling?
a) European Union...
asked 3 hours ago -
A 8.15- g bullet from a 9-mm pistol has a velocity of 366.0 m/s.
It strikes...
asked 4 hours ago -
The outstanding bonds of Alpha Extracts have a yield to maturity
of 7.4 percent and a...
asked 4 hours ago -
The Problem: The Case of the Harmonizing Vacations
Your CEO is exploring partnering with a European...
asked 6 hours ago -
A chemical equation is balanced by adding coefficients in front
of some formulas so that the...
asked 6 hours ago -
From the literature (reference your sources): What are the
lattice parameters of calcite and aragonite? Why...
asked 6 hours ago -
Your system is rejecting the question am asking which is
preceded by a case study. It...
asked 7 hours ago -
3. On January 2, 2000, Larry creates a trust with himself as
trustee. Larry as trustee...
asked 7 hours ago