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!)
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...
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
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) 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...
1) A consumer's utility function is 3r3 3y Prices are Pa-2,Py - 32 (a) Find the consumer's optimal choice for x, y as functions of income I (b) Sketch the demand curves for x, y as functions of income I.