The production function for a commodity is given by Q=43x4 y , with -1<a<0 and -1<B<0...
8 Consider the following 3-input version of a Cobb-Douglas production function y Axxx A 0, 0a, B, y < 1 Find the first- and second-order partial derivatives, and determine the signs. What is the economic interpretation of the signs of these derivatives?
3. (10 points) Consider the utility function U(q;θ) = q1−θ−1, where 0 < θ < 1 is a utility parameter. (a) Compute the marginal utility function, MU(q; θ) = U0(q; θ). (b) Show that MU(q; θ) is decreasing. 3. (10 points) Consider the utility function U(g; e )-Te 1, where 0 < θ < 1 is a utility parameter. (a) (5 points) Compute the marginal utility function, MU(q:e) U'(q;e) (b) (5 points) Show that MU(q:0) is decreasing.
Let the production function be q=ALK. The function exhibits increasing returns to scale if O A. a + b < 1 O B. a + b > 1 OC. a + b = 1 O D. Cannot be determined with the information given
< 1. The joint probability density function (pdf) of X and Y is given by for(x, y) = 4 (1 - x)e”, 0 < x <1, 0 < (a) Find the constant A. (b) Find the marginal pdfs of X and Y. (c) Find E(X) and E(Y). (d) Find E(XY).
Question 7 Consider the following production function: Q=AL' K• Assume A > 0. Further assume 0 <a <1, and 0 <b<1. 1. What is the Marginal Product of Labor (MPL)? Is it diminishing as L increases? What is the Marginal Product of Capital (MPK)? Is it diminishing as K increases? 2. What is the Average Product of Labor (APL)? What is the Average Product of Capital (AP)? 3. What is the TRSL,K? Is the absolute value of TRSL K diminishing...
4. The joint distribution of X and Y is given by 0 otherwise (a) Are X and Y independent? Explairn. (b) Find the marginal probability function (pdf) of Y, fy (). (c) Provide the integral for finding P(X < Y), but DO NOT evaluate.
the joint probability density function is given by 1. The joint probability density function (pdf) of X and Y is given by fxy(x,y) = A (1 – xey, 0<x<1,0 < y < 0 (a) Find the constant A. (b) Find the marginal pdfs of X and Y. (c) Find E(X) and E(Y). (d) Find E(XY).
3. Given the consumption function C = 0 -by (with a > 0:0 <b< 1): (0) Find its marginal function and its average function. (b) Find the income elasticity of consumption Ecy, and determine its sign, assuming Y >0. (9) Show that this consumption function is inelastic at all positive income levels.
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?
Q. Suppose the joint probability density function of X and Y is (a) Show that the value of constant ?=12/11 (b) Find the marginal density function of X, i.e., fX(x). (c) Find the conditional probability density of X given Y = y, i.e., fX|Y(x|y). fxy(x, y) = s k(2 - x + y)x 1 0 0 < x < 1,0 = y = 1 otherwise