U= X13 X24
P1= 4 P2= 1 M=100
P1X1 + P2X2 = M
What is the espression for the inverse demand function for X1?
- Use L= X13 X24 - λ (P1X1 + P2X2 - M)
What is the expression for the engel curve for X1?
Now minimize P1x1 + P2x2 such that U(x1; x2) = x 3 4 1 x 1 4 2 u and x1; x2 0 (a) Using optimization techniques, nd the Hicksian Demand (Z(p; u))Now minimize P1x1 + P2x2 such that U(x1; x2) = x 3 4 1 x 1 4 2 u and x1; x2 0 (a) Using optimization techniques, nd the Hicksian Demand (Z(p; u))Now minimize P1x1 + P2x2 such that U(x1; x2) = x 3 4 1 x 1...
2*. Assume that Bob has a budget constraint p1x1 + p2x2 = m, and that his preferences are represented by the Cobb-Douglas utility function U(x1, x2) = x1 c x2 d , where c>0 and d>0. State Bob’s optimization (utility maximization) problem. a) Set up the Lagrangian function. b) Derive the necessary conditions (the first-order conditions) for an optimal interior solution. c) Show that the MRS (the slope of the indifference curve) is equal to the slope of the budget...
2*. Assume that Bob has a budget constraint p1x1 + p2x2 = m, and that his preferences are represented by the Cobb-Douglas utility function U(x1, x2) = x1 c x2 d , where c>0 and d>0. State Bob’s optimization (utility maximization) problem. a) Set up the Lagrangian function. b) Derive the necessary conditions (the first-order conditions) for an optimal interior solution. c) Show that the MRS (the slope of the indifference curve) is equal to the slope of the budget...
The utility function is u = x1½ + x2, and the budget constraint is m = p1x1 + p2x2. Derive the optimal demand curve for good 1, x1(p1, p2), and good 2, x2(m, p1, p2). Looking at the cross price effects (∂x1/∂p2 and ∂x2/∂p1) are goods x1 and x2 substitutes or complements? Looking at income effects (∂x1/∂m and ∂x2/∂m) are goods x1 and x2 inferior, normal or neither? Assume m=100, p1=0.5 and p2=1. Using the demand function you derived in...
The utility function is u = 3x1 + x2, and the budget constraint is m = p1x1 + p2x2. a) What are the demand functions x1(m,p1,p2) and x1(m,p1,p2)? For m=100, p1=4 and p2=1, what are the consumption amounts x1 and x2? b) Assume only p1 changes to p1’=2, define the new consumption values as x1M and x2M. c) Define as uH the utility amount you get from consumption bundle in part a. Find the consumption bundle (x1H,x2H) that gives you...
Find the optimal bundle for the following utility functions and for budget line (P1X1+P2X2=m) a) U(X1,X2)=X1X2 b) U(X1,X2)=X1^2X2^3 c) U(X1,X2)=X1^2+2X2 d)U(X1,X2)= ln (x1^3X2^4) e) U(X1,X2)= 2X1+X2 f) U(X1,X2)= min (2X1,X2)
1. (Consumer theory) Consider the utility function u(x) = √x1 + √x2 ; and a standard budget constraint: p1x1+p2x2=I. a. Are the preferences convex? (1 pt) b. Are the preferences represented by this function homothetic? (1 pt) c. Formally write the utility maximization problem, derive the first order conditions and find the Marshallian demand function. (2 pt) d. Verify that the demand function is homogeneous of degree 0 in prices and income. (1 pt) e. Find the indirect utility function. (1 pt) f. Find the expenditure function by...
Suppose an individual’s utility function is u=x11/2, x21/2. Let p1=4, p2=5, and income equal $200. With a general equation and general prices, derive the equal marginal principle. Graphically illustrate equilibrium and disequilibrium conditions and how consumers can reallocate their consumption to maximize utility. What is the optimal amount of x1 consumed? What is the optimal amount of x2 consumed? What is the marginal rate of substitution at the optimal amounts of x1 and x2? As functions of p1, p2, and...
Q6 Deriving Demand Function Derive demand functions x1(P1, P2, m) and x2(P1, P2, m) for the consumer with the utility function U(x1, x2) = xi x2
how did they dervice that to get 1/x1=p1/p2 income goes entirely to the consumption of good 2. If quasilinear, we sometimes say that there is a "zero income e income doesn't Thus the Engel curve for good 1 is a vertical line the demand for good 1 remains constant. For example, let us calculate the demand functions for t as yo u(x1, 2)= In a1+x2. Applying the first-order condition gives P1 P2