What is the marginal rate of substitution for U = 0.25*ln(F) + 0.75*ln(X)?
Find the values of F and X with a budget constraint of 560 = F + X
What is the marginal rate of substitution for U = 0.25*ln(F) + 0.75*ln(X)? Find the values...
Utility Function: U = ln (x) + ln (z) Budget Constraint: 120 = 2x + 3z (a) Find the optimal values of x and z (b) Explain in words the idea of a compensating variation for the case where the budget constraint changed to 120 = 2x + 5z Problem 4 (a) Derive the demand functions for the utility function (b) Let a = 2, b = 5, px = 1, pz = 3, and Y = 75. Find the...
Utility Function: U = ln (x) + ln (z) Budget Constraint: 120 = 2x + 3z (a) Find the optimal values of x and z (b) Explain in words the idea of a compensating variation for the case where the budget constraint changed to 120 = 2x + 5z
4. Consider the utility function U(x, y) = x + ln y. (a) Find the marginal rate of substitution, MRS of this function. Interpret the result (b) Find the equation of the indifference curve for this function (c) Compare the marginal utility of x and y. How do you interpret these functions? How might a consumer choose between x and y as she tries to increase utility by, for example, consuming more when their income increases?
4. Consider the utility function U(x,y) -Iny (a) Find the marginal rate of substitution, MRS of this function. Interpret the result (b) Find the equation of the indifference curve for this function (c) Compare the marginal utility of x and y. How do you interpret these functions? How might a consumer choose between z and y as she tries to increase utility by, for example, consuming more when their income increases?
QUESTION 2 Find the Marginal Rate of Substitution (MRSxy) of a consumer with preferences described by U(x, y) = ln(2x + y). c. MRSxy=0.5 MRSxy=2 MRSxy = ? MRSxy = 2x+y None of the above 1 QUESTION 3 A consumer has preferences represented by utility function U(x, y) = x+y. The initial prices are Px = 1 and Py = 2, while initial income is 12. Find the income effect associated with an increase in the price of x to...
Phil’s quasi-linear utility function U (q1q2)= ln q1 + q2. Show that tis marginal rate of substitution (MRS) is the same in all of his indifference curves at given q1.
7. (4 Points) Describe what the marginal rate of substitution of x for Y (MRSxy) to us about a consumer's preferences between the two goods. 8 (4 Points) Suppose you have preferences over two goods, bottles of wine (good X) and slices of pizza (good Y). Explain what it means that for the bundle A = (3, 15), the MRSxy = 2. 9. For this question, use the utility function U(X,Y)= XY. (a) (2 Points) What is the marginal utility...
1. Suppose f(K,L)=[L+K]3, what is the MRTS? 2. Suppose f(K,L)=K(1/2)+L(1/2) Find the marginal rate of technical substitution. 3. f(K,L)=K(1/2)+L(1/2) Find the marginal rate of technical substitution.
The Implicit Function Theorem and the Marginal Rate of Substitution (4 Points) 3 An important result from multivariable calculus is the implicit function theorem which states that given a function f (x,y), the derivative of y with respect to a is given by where of/bx denotes the partial derivative of f with respect to a and af/ay denotes the partial derivative of f with respect to y. Simply stated, a partial derivative of a multivariable function is the derivative of...
3. Given a utility function U(x, y) -rys, (a) Show that the marginal rate of substitution, MRS (b) For commodity bundles for which y how does the MRS depend on the values of α and β? Develop an intuitive explanation of why, if α > β, MRS > 1.