Just 3.4 and 3.5 please Question 3Consider the following system of production functions for firm i which produces two outputs,namely good 1 and good 2:91(K, L) = 5K1/8 L7/8(3)= 4(-K/2 + L!/2)2(4)where q1 is the quantity produced of good 1, q2 is the quantity produced of good 2, K is capitaland L is labour.3.1 Calculate an equation for the marginal rate of technical substitution (MRTS) for theproduction of good 1 (91) in order to illustrate how much more labour L the firm wouldrequire to compensate for losing 1 unit of capital K while remaining on the same isoquant.You need not evaluate the MRTS at a specific point.3.2 If the firm is currently producing where K = 2 and L = 2 and would like to increaseproduction of good 1 (q1) as rapidly as possible, in what ratio should it increase its currentlevels of inputs of K and L in order to reach a higher isoquant? Present your answer as aunit vector (i.e. a vector of length 1).3.3 Suppose again that the firm is producing where K = 2 and L = 2. Set up the Jacobianderivative matrix to approximate the rate of change in Q(q1, 42) for changes in K and Lat this point on the production function.dqi3.4 Now, using the Jacobian derivative matrix and matrix algebra, calculate the vectorifdq2the firm decides to increase K by 5 units and decrease L by 0.2 units.3.5 Construct the Hessian matrix for equation (3). Using the information contained in theHessian matrix, does the firm have increasing or diminishing marginal productivity forgood 1 (g1)? You need not evaluate the Hessian matrix at a specific point.

Production function:Production is a function of land labor capital and entrepreneurship. It includes…

3.4 Now, using the Jacobian derivative matrix and matrix algebra, calculate the vector the firm decides to increase K by 5 units and decrease L by 0.2 units. dq₁ dq2 if 3.5 Construct the Hessian matrix for equation (3). Using the information contained in the Hessian matrix, does the firm have increasing or diminishing marginal productivity for good 1 (91)? You need not evaluate the Hessian matrix at a specific point.

3.4 Now, using the Jacobian derivative matrix and matrix algebra, calculate the vector the firm decides to increase K by 5 units and decrease L by 0.2 units. dq₁ dq2 if 3.5 Construct the Hessian matrix for equation (3). Using the information contained in the Hessian matrix, does the firm have increasing or diminishing marginal productivity for good 1 (91)? You need not evaluate the Hessian matrix at a specific point.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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