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.)
a. At Optimal point, MUx/MUy=Px/Py
y/(x+10)=Px/Py
y=Px*(x+10)/Py... put this in Budget constraint
X*Px+Y*Py=I
X*Px+Py*(Px*(x+10)/Py)=I
X*Px+X*PX+10Px=I
2XPx=I-10Px
X*=(I-10Px)/2Px
X*= I/2Px-5
b. X*=100/2Px -5= 50/Px-5
For X* to be positive, maximum value of Px should be less than 10.
When Px=10, X*=0.
Suppose that a consumer’s utility function is U(x,y)=xy+10y. the marginal utilities for this utility function are...
1. Utility is given by U(x, y) = xy + 10y, with marginal utilities MU, = y and MU, = x + 10. The price of r is Px and the price of y is Py. The consumer has income m. (a) Assume first that we have an interior solution. Solve for the demand for r. (b) Suppose now that m= 100. Since x must never be negative, what is the maximum price for good x for which this consumer...
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...
clear writing please 1. Utility is given by U(x,y) = y + 10y, with marginal utilities MU, = y and MU, = x + 10. The price of x is P, and the price of y is Py. The consumer has income m. (a) Assume first that we have an interior solution. Solve for the demand for u. (b) Suppose now that m = 100. Since I must never be negative, what is the maximum price for good x for...
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...
4) A consumer’s utility function is u(x, y) = min{x, 3y} (a) Find the consumer’s optimal choice for x, y as functions of income I and prices px,py. (b) Sketch the demand curve for y as a function of other price px when py = 10, I = 100. Suggestion: a picture showing the budget set, optimal choice and indifference curve. (I need help with the sketching which is the second part)
2) A consumer’s utility function is u(x,y)=-1/3x^3 - 1/y (a) Find the consumer’s optimal choice for x as a function of income I and prices px,py.
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?...
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)...
Suppose there are two consumers, A and B, and two goods, X, and Y. Consumer A's utility function is given by: Ua(X,Y) = X*Y^3 Consumer B's utility function is given by: Ub (X,Y) = X*Y Marginal Utilities for A: MUx =Y^3 , MUy = 3X*Y^2 Marginal Utilities for B: MUx = Y, MUy = X Initial endowments: Person A has 40 units of good X and 20 units of good Y Person B has 30 units of good x and...
Suppose James derives utility from two goods {x,y}, characterised by the following utility function: $u(x, y) = 2sqrt{x} + y$: his wealth is w = 10 let py = 1: (a) What is his optimal basket if px = 0.50? What is her utility? (b) What is his optimal basket and utility if px = 0.20? (c) Find the substitution effect and the income effect associated with the price change. (d) What is the change in consumer surplus? Suppose Linda...