Answer:
Lorelai's choice behavior can be represented by the utility function 11(xi, X2) = 0.91n(xi) + 0.1x2...
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...
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...
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....
4. Anne's utility function is given by u(xi,x2) Michael's utility function is given by u(xı, x2)' = x1x2. She has two friends, Michael and Peter 1 and Peter's is given by u(x1, X2) = = 1042 1 Τ) -x12. Who has the same preferences as Anne? And who has indifference curves with similar shape as Anne's indifference curves? Explain. 4. Anne's utility function is given by u(xi,x2) Michael's utility function is given by u(xı, x2)' = x1x2. She has two...
how did they get MRS= -x2/x1? Consider the utility function u ( 2 2) = Inc. +Inc. Suppose that the initial situation s given by Pi = 1, P2 = 2 and m = 100. Note that MU = 1 and MU2 = a) Find the consumer's optimal consumption bundle (0,2) and his utility at this consumption bundle. Solution: The budget line is 2.02 = 100 - 21 (1) Since the optimal bundle is an interior point, the tangency condition...
Question 4: Consider a general utility function U(xi, x2). Let's now solve for the optimal bundle generally using the Lagrangian Method. 1. Write down the objective function and constraint in math 2. Set up the Lagrangian Equation 3. Fnd the first derivatives. 4, Find the first order conditions, what's the interpretation for λ? 5. Rearrange them to get the tangency condition.
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...
Furthermore, let the price of x1 be $1 and the price of x2 be $4, while his income is fixed at $20. a) Graph the budget line with x1 on the x axis and x2 on the y-axis. (1 Marks) b) On the same sketch above, graph two indifference curves. (Be careful about the rate of substitution between both x1 and x2 and hence the slopes of the indifference curves). (2 Marks) c) What is the optimal bundle chosen by...
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...
4. Andy's utility is represented by the function U(X,Y) - XY. His marginal utility of X is MUx = Y. His marginal utility of Y is MUY = . He has income $12. When the prices are Px - 1 and Py -1, Andy's optimal consumption bundle is X* -6 and Y' = 6. When the prices are Px = 1 and P, = 4, Andy's optimal consumption bundle is X** = 6 and Y* 1.5. Suppose the price of...