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5. A consumer faces a standard linear budget constraint and has preferences that can be represented...
3. Suppose an individual has perfect-complements preferences that can be represented by the utility function U(x,y)=...
3. Suppose an individual has perfect-complements preferences that can be represented by the utility function U(x,y)= min[3x,2y]. Furthermore, suppose that she faces a standard linear budget constraint, with income denoted by m and prices denoted by px and p,, respectively. a) Derive the demand functions for x and y. b) How does demand for the two goods depend on the prices, p, and p, ? Explain.
A consumer with convex, monotonic preferences consumes non-negative amount of and . This consumer faces the...
A consumer with convex, monotonic preferences consumes
non-negative amount of
and
. This consumer faces the budget constraint
and has the utility function
a) What is the restrictions on the value of
such that this person is an ordinary and rational consumer?
Why?
b) Given those restrictions on
, derive the Marshallian demand functions of the consumer.
c) What is elasticity of substitution? Explain in your own words
the concept of elasticity of substitution.
d) Calculate and interpret the elasticity...
A consumer with convex, monotonic preferences consumes non-negative amount of and . This consumer faces the...
A consumer with convex, monotonic preferences consumes
non-negative amount of
and
. This consumer faces the budget constraint
and has the utility function
where
a) Derive the indirect utility function.
b) Derive the expenditure function.
c) Explain briefly according to your understanding the link
between direct, indirect and expediture function.
We were unable to transcribe this imageWe were unable to transcribe this image2121 +22p2 <y u(r1, 72) = riz-a 0 <α<
2*. Assume that Bob has a budget constraint p1x1 + p2x2 = m, and that his...
2*. Assume that Bob has a budget constraint p1x1 + p2x2 = m, and that his preferences are represented by the Cobb-Douglas utility function U(x1, x2) = x1 c x2 d , where c>0 and d>0. State Bob’s optimization (utility maximization) problem. a) Set up the Lagrangian function. b) Derive the necessary conditions (the first-order conditions) for an optimal interior solution. c) Show that the MRS (the slope of the indifference curve) is equal to the slope of the budget...
2*. Assume that Bob has a budget constraint p1x1 + p2x2 = m, and that his...
2*. Assume that Bob has a budget constraint p1x1 + p2x2 = m, and that his preferences are represented by the Cobb-Douglas utility function U(x1, x2) = x1 c x2 d , where c>0 and d>0. State Bob’s optimization (utility maximization) problem. a) Set up the Lagrangian function. b) Derive the necessary conditions (the first-order conditions) for an optimal interior solution. c) Show that the MRS (the slope of the indifference curve) is equal to the slope of the budget...
Problem 2 A consumer has the following preferences regarding consumption and leisure time: ?(?, ?) =...
Problem 2 A consumer has the following preferences regarding consumption and leisure time: ?(?, ?) = ? ∙ (24 − ?) Where ? is the quantity of an aggregated consumption good and ? are the supplied labour hours (working in a job) per day, and consequently, 24 − ? is the leisure time ?. The budget available for daily consumption is the sum of labour income and other fixed (daily) income with ? = price of the aggregated consumption good...
A consumer has preferences represented by the utility function u(x, y) -xlyi. (This means that a....
A consumer has preferences represented by the utility function u(x, y) -xlyi. (This means that a. What is the marginal rate of substitution? b. Suppose that the price of good x is 2, and the price of good y is 1. The consumer's income is 20. What is the optimal quantity of x and y the consumer will choose? c. Suppose the price of good x decreases to 1. The price of good y and the consumer's income are unchanged....
Question 2 Question 2 (15 pts) A consumer has preferences represented by the utility function u(x,y)...
Question 2
Question 2 (15 pts) A consumer has preferences represented by the utility function u(x,y) -xlyi. (This means that a. What is the marginal rate of substitution? b. Suppose that the price of good x is 2, and the price of good y is 1. The consumer's income wWhat is the optimal quantity is 20. What is the optimal quantity of x and y the consumer will choose? c. Suppose the price of good x decreases to 1. The...
Question 2 (15 pts) A consumer has preferences represented by the utility function ufa,y)ty. (This means...
Question 2 (15 pts) A consumer has preferences represented by the utility function ufa,y)ty. (This means that Muy and Muy ly 1) a. What is the marginal rate of substitution? b. Suppose that the price of good x is 2, and the price of good y is 1. The consumer's income is 20. What is the optimal quantity of x and y the consumer will choose? c. Suppose the price of good x decreases to 1. The price of good...
Suppose there are two consumption goods and preferences of a consumer can be represented by the following utility functi...
Suppose there are two consumption goods and preferences of a
consumer can be represented by the following utility function:
;
a) Derive the Marshallian demand function of this consumer.
b) Calculate and intuitively interpret the elasticity of
substitution.
d/11027(0 - 1) + 10) = (2x Iz)n (0<a <1:0 +p<1)
3. Suppose an individual has perfect-complements preferences that can be represented by the utility function U(x,y)= min[3x,2y]. Furthermore, suppose that she faces a standard linear budget constraint, with income denoted by m and prices denoted by px and p,, respectively. a) Derive the demand functions for x and y. b) How does demand for the two goods depend on the prices, p, and p, ? Explain.
A consumer with convex, monotonic preferences consumes
non-negative amount of
and
. This consumer faces the budget constraint
and has the utility function
a) What is the restrictions on the value of
such that this person is an ordinary and rational consumer?
Why?
b) Given those restrictions on
, derive the Marshallian demand functions of the consumer.
c) What is elasticity of substitution? Explain in your own words
the concept of elasticity of substitution.
d) Calculate and interpret the elasticity...
A consumer with convex, monotonic preferences consumes
non-negative amount of
and
. This consumer faces the budget constraint
and has the utility function
where
a) Derive the indirect utility function.
b) Derive the expenditure function.
c) Explain briefly according to your understanding the link
between direct, indirect and expediture function.
We were unable to transcribe this imageWe were unable to transcribe this image2121 +22p2 <y u(r1, 72) = riz-a 0 <α<
A consumer has preferences represented by the utility function u(x, y) -xlyi. (This means that a. What is the marginal rate of substitution? b. Suppose that the price of good x is 2, and the price of good y is 1. The consumer's income is 20. What is the optimal quantity of x and y the consumer will choose? c. Suppose the price of good x decreases to 1. The price of good y and the consumer's income are unchanged....
Question 2
Question 2 (15 pts) A consumer has preferences represented by the utility function u(x,y) -xlyi. (This means that a. What is the marginal rate of substitution? b. Suppose that the price of good x is 2, and the price of good y is 1. The consumer's income wWhat is the optimal quantity is 20. What is the optimal quantity of x and y the consumer will choose? c. Suppose the price of good x decreases to 1. The...
Question 2 (15 pts) A consumer has preferences represented by the utility function ufa,y)ty. (This means that Muy and Muy ly 1) a. What is the marginal rate of substitution? b. Suppose that the price of good x is 2, and the price of good y is 1. The consumer's income is 20. What is the optimal quantity of x and y the consumer will choose? c. Suppose the price of good x decreases to 1. The price of good...
Suppose there are two consumption goods and preferences of a
consumer can be represented by the following utility function:
;
a) Derive the Marshallian demand function of this consumer.
b) Calculate and intuitively interpret the elasticity of
substitution.
d/11027(0 - 1) + 10) = (2x Iz)n (0<a <1:0 +p<1)
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