5. Melissa’s utility function for the bundle (x,y) is U(x,y)=xy. Price of good x is p1=1, price of good 2 is p2=2 and income m=10. If the price of good 1 goes up to p1=2, but the rest remain the same.
Derive: Total effect? Substitution effect? Income effect?
5. Melissa’s utility function for the bundle (x,y) is U(x,y)=xy. Price of good x is p1=1, price of good 2 is p2=2 and income m=10. If the price of good 1 goes up to p1=2, but the rest remain the same....
3. (10 points) Income and substitution effects A consumer's utility is given by U(x, y) = xy. Income is m and prices are given by p and Py (a) Find the demand functions for x and y. (b) What is demand for each good if p 2 and py 1 and income is m = (c) If price of x fell to pa 1, what is the consumer's new bundle? (d) How much of the response in the consumption of...
Suppose that a consumer’s utility function is U=xy with MUx=y and MUy=x. Suppose the consumer‘s income is $480. For this question you may need to use the following approximations: sqrt(2) is approximately 1.4, sqrt(3) is approx. 1.7 and sqrt(5) is approx 2.2. a) Initially, the price of y is $4 and the price of x is $6. What is the consumer’s optimal bundle? b) What is the consumer's initial utility? Now suppose that price of x increases to $8 and...
7. Jay's Utility function is given by U(x,z) = 3x10.2 x20.8 and P1=$2 and P2=$4 and his budget is $200. Write out the Lagrange but DO NOT solve it Find the utility maximizing values of x1and x2 8. What does the substitution effect cause a consumer to do if the price of a good increases? 9. What does the income effect cause a consumer to do if the price of a good increases? What else is needed here? 10. What...
Imagine you consume two goods, X and Y, and your utility function is U = XY. Your budget is $100, the price of Good X is $4, and the price of Good Y is $25. So, the optimal bundle for you to consume is (12.5, 2). Now the price of good X increases to $10. The compensated price bundle is (7.91, 3.16). What is the income effect on X?
Given a utility function U(x,y) = xy. The price of x is Px, while the price of y is Py. The income is I. Suppose at period 0, Px = Py = $1 and income = $8. At period 1, price of x (Px) is changed to $4. Compute the price effect, substitution effect, and income effect for good x from the price change.
5. A consumer's preferences are given by the utility function U-2 2 The price of good 1 is 3 and the price of 2 is 6, while her income is 36. The utility maximising bundle for the consumer is a. xi = 4, = 4 b. x1 = 4,=3 c. ri = 2 = 6 d. x = 8,5 = 2 e. None of the above 6. A consumer's preferences are given by the utility function U = . The...
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...
* * 5. A consumer's preferences are given by the utility function U = x;'°*". The price of good 1 is 3 and the price of 2 is 6, while her income is 36. The utility maximising bundle for the consumer is a. X* = 4, x* = 4 b. x1 = 4, x = 3 C. x1 = 2, x = 6 d. x1 = 8, x* = 2 e. None of the above * * N * *...
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...
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...