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)
4) A consumer’s utility function is u(x, y) = min{x, 3y} (a) Find the consumer’s optimal...
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.
3) A consumer's utility function is u(x,y)22 (a) Find the consumer's optimal choice for x, y as functions of income I and (b) Sketch the demand curves for x, y as functions of income I when prices prices pa,Py. (Be careful!) are p 16,Py 2. (Be careful!)
3) A consumer's utility function is 2y (a) Find the consumer's optimal choice for x, y as functions of income I and prices px,py. (Be careful!) (b) Sketch the demand curves for x, y as functions of income I when prices are px = 16, p,-2. (Be careful!)
4) A consumer's utility function is (a) Find the consumer's optimal choice for x, y as functions of income I and prices pa,Pv. 10 (b) Sketch the demand curve for y as a function of other price pz when py I-100
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...
2) A consumer's utility function is a(x,y) = (a) Find the consumer's optimal choice for x as a function of income I and prices px,Py' (b) Sketch the demand curve for x as a function of its own price Pz when py = 10, 1 = 100. (It may be easiest to plot a few points.)
. A consumer’s utility function is given by U(x, y) = 4x^1/2 + y^1/2 The consumer’s income is M, the price of good y is Py and the price of good x is Px. (Warning: the algebra in this problem is messy but it is good practice.) (a) What is the marginal rate of substitution? (b) What is the equation for the budget constraint? (c) What is the demand function for x (as a function of prices and income)?
A) Suppose U = min[X, 3Y] and I=12, Px=1 and Py=5. Find X* and Y*. B) Draw an indifference curve and a normal linear budget constraint such that there is a tangency point (where MRS= price ratio) that is not the optimal bundle. C) Suppose U=X∙Y5. Find X* and Y*. D) Suppose U = 5∙X + 2∙Y and I=12, Px=2 and Py=1. Find X* and Y*.
2. Consider a utility function that represents preferences: u(x,y)= min{80x,40y} Find the optimal values of x and y as a function of the prices px and py with an income level m. (5)
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...