2. Which of the following is NOT a monotonic transformation of U =
x1x2 for x1 >0,x2 >0.
a. V =U2
b. V = 2U
c. V =U −10
d. V =U3
e. All of the above (a, b, c, d) are monotonic transformations
2. Which of the following is NOT a monotonic transformation of U = x1x2 for x1...
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)
Do the following utility functions represent the same
preferences? Please provide your reasoning
(a) u(X1; XY) = X1 X2, V(X; X2) = 3(x] X2)2 +6 (b) u(x]; X») = X1X2, V(X]; X2) =-3(x1x2)2 +6 (c) u(x1,x2)=X]X2,v(x1,x2)=lnx1 +lnx2 (d) u(x]; X) = X1 X2, V(X1; X2) = x1 + x2
1. Consider the utility function: u(x1,x2) = x1 +x2. Find the corresponding Hicksian demand function 2. For each of the three utility functions below, find the substitution effect, the income effect, and the total effect that result when prices change from p = (2,1) to p' = (2,4). Assume the consumer has income I = 20. (a) Before doing any calculation, make an educated guess about the relative magnitude of the three substitution effects and the three income effects to be found below. (b)...
Let X1 d = R(0,1) and X2 d= Bernoulli(1/3) be two independent random variables, define Y := X1 + X2 and U := X1X2. (a) Find the state space of Y and derive the cdf FY and pdf fY of Y . (You may wish to use {X2 = i}, i = 0,1, as a partition and apply the total probability formula.) (b) Compute the mean and variance of Y in two different ways, one is through the pdf of...
2. For the following economies find the set of all efficient allocations: (a) Preferences are u'(x1, x2) = min{x\, x2}, u2(x1, 2) = min{x1,X2}. Endowments are i. e! %3D (3,6), е? ii. et %3D (5, 7), е? %3 (15, 3); ii. e' %3D (5, 7), е? %3D (25, 3). (b) As in part (a), but u'(r\, x2) = max{x1, x2} (7,4); 3. Find the Walrasian Equilibrium price(s) and allocations for all the economies in Question 1 and 2
2. For...
1. Consider the utility function: u(x1,x2) = x1 + x2. Find the corresponding Hicksian demand function. 2. For each of the three utility functions below, find the substitution effect, the income effect, and the total effect that result when prices change from p =(2, 1) to p' = (2,4). Assume the consumer has income I = 20. (a) Before doing any calculation, make an educated guess about the relative magnitude of the three substitution effects and the three income effects...
1. Consider the utility function: u(x1,x2) = x1 + x2. Find the corresponding Hicksian demand function. 2. For each of the three utility functions below, find the substitution effect, the income effect, and the total effect that result when prices change from p = (2,1) to p' = (2,4). Assume the consumer has income I = 20. (a) Before doing any calculation, make an educated guess about the relative magnitude of the three substitution effects and the three income effects...
9/: then the Jacobian of the transformation J(u, v) in 2. Ifs= vj and v= (A) 2u/v (B) tua (D) 0
Question 4 Which of the following statements about the technical rate of substitution is false? (A) It is positive for monotonic production technologies. (B) It measures the slope of an isoquant. (C) It measures the degree to which inputs are substitutable for each other in the pro- duction process. (D) It equals the negative of two inputs' marginal products. (E) The phenomenon of diminishing technical rate of substitution reflects the idea that an input can be replaced more easily when...
9. A triangle is described by its "corners" in the order (< x1, yı >, < x2, Уг >, < x31%-) and drawn on a display screen using lines from < xı'yı > to < x2,Y2 >; < x2,U2 > to < x3,U3 >; and, finally, from < x3, уз > to < x1, yı > . A 3 3 matrix. 1 0 10 0 1 -20 is used to move this shape 10 places right and 20 places down....