Luke's choice behavior can be represented by the utility function u(x1,x2)= x1 + x2
Luke's choice behavior can be represented by the utility function u(x1,x2)= x1 + x2.The prices of x1 and x2 are denoted as p1 and p2, and his income is m.
1. Draw at least three indifference curves and find its slope (i.e. MRS). Is the MRS changing depending on the points of (x1, x2) at which it is evaluated, or constant?
2. Draw a budget constraint assuming that p1 < P2. Find the optimal bundle (x1*,x2*) as a function
of income and prices.
3. Draw a budget constraint assuming that p1 > P2. Find the optimal bundle (x1*, x2*) as a function of income and prices.
4. Draw a budget constraint assuming that p1 = P2. Find the optimal bundle (x1*, x2*) as a function of income and prices.
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Luke's choice behavior can be represented by the utility function u(x1,x2)= x1 + x2
Lorelai's choice behavior can be represented by the utility function u(x1, 2) 0.9n(x)0.1x2. The prices of...
Lorelai's choice behavior can be represented by the utility function u(x1, 2) 0.9n(x)0.1x2. The prices of both xi and x2 are $5 and she has an income of $40. 1. What preference does this utility function represent? (Hint: the utility is function is not linear, but at least linear in good x2) 2. Drawinwg indifference curves: you can copy down the graph on your paper using econgraphs. Set the preferences and parameters accordingly as given in the question. Click on...
Question 2: Lorelai's choice behavior can be represented by the utility function u(x1, 2)0.9Inx)0.1x2 The prices...
Question 2: Lorelai's choice behavior can be represented by the utility function u(x1, 2)0.9Inx)0.1x2 The prices of both x1 and x2 are $5 and she has an income of $40. 1. What preference does this utility function represent? (Hint: the utility is function is not linear, 2. Drawinwg indifference curves: you can copy down the graph on your paper using econgraphs. Set but at least linear in good x2) the preferences and parameters accordingly as given in the question. Click...
Consider a consumer with a utility function u(x1, x2) = min{21, 222}. Suppose the prices of...
Consider a consumer with a utility function u(x1, x2) = min{21, 222}. Suppose the prices of good 1 and good 2 are p1 = P2 = 4. The consumer's income is m = 120. (a) Find the consumer's preferred bundle. (b) Draw the consumer's budget line. (c) On the same graph, indicate the consumer's preferred bundle and draw the indifference curve through it. (d) Now suppose that the consumer gets a discount on good 1: each unit beyond the 4th...
Lorelai's choice behavior can be represented by the utility function 11(xi, X2) = 0.91n(xi) + 0.1x2...
Lorelai's choice behavior can be represented by the utility function 11(xi, X2) = 0.91n(xi) + 0.1x2 The prices of both x and x2 are $5 and she has an income of $40. 1. What preference does this utility function represent? (Hint: the utility is function is not linear, but at least linear in good x2.) 2. Drawinwg indifference curves: you can copy down the graph on your paper using econgraphs. Set the preferences and parameters accordingly as given in the...
2. 2.1 Draw the indifference curves for the utility function U(21, 22) = x1 + 3x2....
2. 2.1 Draw the indifference curves for the utility function U(21, 22) = x1 + 3x2. 2.2 What is the marginal rate of substitution evaluated at an arbitrary consumption bundle (21, 22)? 2.3 Suppose that p1 = 5, P2 = 2, and M = 10. Find the utility-maximizing consump- tion bundle (among those that satisfy the budge constraint) for this agent. You should be able to do this without using any calculus: it should be clear from your indifference curves....
Suppose Alex’s preferences are represented by u(x1,x2) = x1x32. The marginal utilities for this utility function...
Suppose Alex’s preferences are represented by u(x1,x2) = x1x32. The marginal utilities for this utility function are MU1 = x23 and MU2 = 3x1x22. (a) Show that Alex’s utility function belongs to a class of functions that are known to be well-behaved and strictly convex. (b) Find the MRS. [Note: find the MRS for the original utility function, not some monotonic transformation of it.] (c) Write down the tangency condition needed to find an optimal consumption bundle for well-behaved preferences....
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...
The utility function is u = 3x1 + x2, and the budget constraint is m =...
The utility function is u = 3x1 + x2, and the budget constraint is m = p1x1 + p2x2. a) What are the demand functions x1(m,p1,p2) and x1(m,p1,p2)? For m=100, p1=4 and p2=1, what are the consumption amounts x1 and x2? b) Assume only p1 changes to p1’=2, define the new consumption values as x1M and x2M. c) Define as uH the utility amount you get from consumption bundle in part a. Find the consumption bundle (x1H,x2H) that gives you...
Yam has the following utility function for Apples (X1) and Ice Cream (X2) U(X1,X2) = Min{3X1,X2}....
Yam has the following utility function for Apples (X1) and Ice Cream (X2) U(X1,X2) = Min{3X1,X2}. Draw Yam’s indifference curves when she consumes 1 and 2 apples. Derive Yam’s demand functions for Apples and Ice Cream. Suppose Yam has an income of M = $120 and the prices of Apples and Ice Cream are p1 =$1, p2 =$1. What is Yam’s optimal consumption of Apples and Ice Cream? Suppose a quantity tax of $1 is imposed on Apples. Separate out the...
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...
Lorelai's choice behavior can be represented by the utility function u(x1, 2) 0.9n(x)0.1x2. The prices of both xi and x2 are $5 and she has an income of $40. 1. What preference does this utility function represent? (Hint: the utility is function is not linear, but at least linear in good x2) 2. Drawinwg indifference curves: you can copy down the graph on your paper using econgraphs. Set the preferences and parameters accordingly as given in the question. Click on...
Question 2: Lorelai's choice behavior can be represented by the utility function u(x1, 2)0.9Inx)0.1x2 The prices of both x1 and x2 are $5 and she has an income of $40. 1. What preference does this utility function represent? (Hint: the utility is function is not linear, 2. Drawinwg indifference curves: you can copy down the graph on your paper using econgraphs. Set but at least linear in good x2) the preferences and parameters accordingly as given in the question. Click...
Consider a consumer with a utility function u(x1, x2) = min{21, 222}. Suppose the prices of good 1 and good 2 are p1 = P2 = 4. The consumer's income is m = 120. (a) Find the consumer's preferred bundle. (b) Draw the consumer's budget line. (c) On the same graph, indicate the consumer's preferred bundle and draw the indifference curve through it. (d) Now suppose that the consumer gets a discount on good 1: each unit beyond the 4th...
Lorelai's choice behavior can be represented by the utility function 11(xi, X2) = 0.91n(xi) + 0.1x2 The prices of both x and x2 are $5 and she has an income of $40. 1. What preference does this utility function represent? (Hint: the utility is function is not linear, but at least linear in good x2.) 2. Drawinwg indifference curves: you can copy down the graph on your paper using econgraphs. Set the preferences and parameters accordingly as given in the...
2. 2.1 Draw the indifference curves for the utility function U(21, 22) = x1 + 3x2. 2.2 What is the marginal rate of substitution evaluated at an arbitrary consumption bundle (21, 22)? 2.3 Suppose that p1 = 5, P2 = 2, and M = 10. Find the utility-maximizing consump- tion bundle (among those that satisfy the budge constraint) for this agent. You should be able to do this without using any calculus: it should be clear from your indifference curves....
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