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 we find that the optimal bundle for the consumer is x*=30 and y*=60.
c) What is the change in the consumer’s demand for good x?
d) What is the change in the consumer’s demand for good y?
e) Using this information, what the cross price elasticity of demand for good y with the price of good x?
f) What is the substitution bundle?
g) What is the substitution and income effect on good x?
Suppose that a consumer’s utility function is U=xy with MUx=y and MUy=x. Suppose the consumer‘s income...
Suppose that a consumer’s utility function is U(x,y)=xy+10y. the marginal utilities for this utility function are MUx=y and MUy=x+10. The price of x is Px and the price of y is Py, with both prices positive. The consumer has income I. (this problem shows that an optimal consumption choice need not be interior, and may be at a corner point.) Assume first that we are at an interior optimum. Show that the demand schedule for x can be written as...
U (x, y) = 3x3 + 6y3 a)Calculate MUx and MUy. b) Do the consumer’s preferences exhibit a diminishing marginal utility for each good? c) Calculate MRSx,y. d) Do the consumer’s preferences exhibit a diminishing marginal rate of substitution of x?
U (x, y) = 3x3/4 + 3y a)Calculate MUx and MUy. b) Do the consumer’s preferences exhibit a diminishing marginal utility for each good? c) Calculate MRSx,y. d) Do the consumer’s preferences exhibit a diminishing marginal rate of substitution of x?
U (x, y) = 4x11/6 y1/6 . a)Calculate MUx and MUy. b) Do the consumer’s preferences exhibit a diminishing marginal utility for each good? c) Calculate MRSx,y. d) Do the consumer’s preferences exhibit a diminishing marginal rate of substitution of x?
U (x, y) = 5x1/3 y2/3 a)Calculate MUx and MUy. b) Do the consumer’s preferences exhibit a diminishing marginal utility for each good? c) Calculate MRSx,y. d) Do the consumer’s preferences exhibit a diminishing marginal rate of substitution of x?
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...
1. Consumer’s utility function is: U (X,Y) = 10X + Y. Consumer’s income M is 40 euros, the price per unit of good X (i.e. Px ) is 5 euros and the price per unit of good Y (i.e. Py) is 1 euro. a) What is the marginal utility of good X (MUx) for the consumer? ( Answer: MUx = 10) b) What is the marginal utility of good Y (MUy) for the consumer? ( Answer: MUy = 1) c)...
7. Lori has the following utility function U = X0.5Y0.5 MUx = 0.5 X-0.5Y0.5 MUy = 0.5 X0.5Y-0.5 A.) Calculate Lori’s optimal consumption bundle when Px = Py = 10 given a budget of 200 B.)Calculate Lori’s optimal consumption bundle if Px = 5, other things equal C.) Derive Lori’s demand for good X assuming it is linear.
Suppose a consumer’s utility function is given by U(X,Y) = X*Y. Also, the consumer has $180 to spend, and the price of X, PX = 4.50, and the price of Y, PY = 2 a. How much X and Y should the consumer purchase in order to maximize her utility? b. How much total utility does the consumer receive? c. Now suppose PX decreases to 2. What is the new bundle of X and Y that the consumer will demand?...
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....