7. Consider the utility function U(11,12)= nei +2y if x > 0 -0 otherwise Assume P1,...
Exercise 1 Consider utility maximization problem: Kuhn Tucker Theorem max U (x1, x2) = x1+x2 21,22 subject to Tị 2 0, r2 > 0, p1x1+p2r2 < I, where p1, p2 and I are positive constants. Exercise 1 Consider utility maximization problem: Kuhn Tucker Theorem max U (x1, x2) = x1+x2 21,22 subject to Tị 2 0, r2 > 0, p1x1+p2r2 < I, where p1, p2 and I are positive constants.
3. Consider the following utility function, u (1, 2) min br 0<a1 and b>0 (a) [15 points] Derive the Marshallian demand functions. (Explain your derivation in details.) Does the Marshallian demand increase with price? consumption goods normal goods? (b) [ 15 points Derive the Hicksian demand functions. Does the icksian demand increase with price?
2.5.6. The probability density function of a random variable X is given by f(x) 0, otherwise. (a) Find c (b) Find the distribution function Fx) (c) Compute P(l <X<3)
5. Consider the indirect utility function given by: m v(P1, P2, m) = P1 + P2 (a) What are the demand functions (b) What is the expenditure function? (c) What is the direct utility function?
Consider a utility function u(x,y) = Xayb, where 0くaく1 and 0 < b 〈 1. Also assume that x,y>0 7.1. Derive the marginal utility of x and the marginal utility of y and state whether or not the assumption that more is better is satisfied for both goods. 7.2. Does the marginal utility of x diminish, remain constant, or increase as the consumer buys more x?What does it mean in words? 7.3. What is MRS.y? 7.4. Suppose a, b- Wht...
Suppose Alex’s preferences are represented by u(x1,x2) = x1x32. The marginal utilities for this utility function are MU1 = x23 and MU2 = 3x1x22. (a) Show that Alex’s utility function belongs to a class of functions that are known to be well-behaved and strictly convex. (b) Find the MRS. [Note: find the MRS for the original utility function, not some monotonic transformation of it.] (c) Write down the tangency condition needed to find an optimal consumption bundle for well-behaved preferences....
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...
Suppose you have following utility function :U(x,y)=(x + yaja where x >0, y>0 and a 70, a <1 The price of commodity x is P >0 and the price of good y is P, > 0. Let us denote income by M, with M>0 a) Compute the marginal utilities of X and Y. b) Write down the utility maximization problem and corresponding Lagrangian function. c) Solve for optimal bundle, X* and y* as a function of Px, Py, and M.
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...
Suppose you have follow ing utility function : UX1,X2)-Xx2 where 0<0<1; 0<B< 1; 0<B+0<1 The price of commodity X, is P, >0; the price of good X, is P, >0 a) Set up the expenditure minimizati on problem. b) Obtain compensated demand curves c) Calculate cross price elasticiti es of demand curves d) Calculate marginal cost of utility e) Obtain the optimal expenditure function Is the expenditure function increasing with respect to prices and utility?