3.
Ans:
We have:
To find total differential, we have:
At optimal point, change in y or dy = 0. So, we have:
After rearranging, we get:
We can see that as x1 rises or x2 falls, MRTS (slope of isoquant) falls which shows that isoquants are striclty convex to origin and look like following:
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3. Use the total differential to find the MRTS for the production function y X1X2. Show...
3. Use the total differential to find the MRTS for the production function y X1X2. Show that the isoquants are strictly convex to the origin.
67. Use the total differential and implicit function derivative to find the MRTS for the produc- tion functions: 1-)32 (b) y Arlr: with A>0, α > 0, β < 1
1. Let P(L, K) 214K3/4 be a Cobb-Douglas production function. Find the MRTS at the point (3, 5) Find the total differential, dP at (81, 16) if dL .2 and dK--.1. 1. Let P(L, K) 214K3/4 be a Cobb-Douglas production function. Find the MRTS at the point (3, 5) Find the total differential, dP at (81, 16) if dL .2 and dK--.1.
12L1/4 K3/4 be a Cobb-Douglas production function. Find the 1. Let P(L, K) MRTS at the point (3,5) Find the total differential, dP at (81, 16) if dL - .2 and dK = -.1. 12L1/4 K3/4 be a Cobb-Douglas production function. Find the 1. Let P(L, K) MRTS at the point (3,5) Find the total differential, dP at (81, 16) if dL - .2 and dK = -.1.
3. Consider the production function y=. Assume r > 1. (a) Show that the production function y(«) is concave. (b) Show that the inverse production function z(y) is convex. (e) The price of y is p= 10. Find the firm's total product TP(x), marginal product MP) and average product AP (a). (d) Find the firm's value of marginal product VMP), and value of average product V AP(x). (e) Assume w<marV AP(x) Find the firm's input demand curve r*(w). (1) Suppose...
3. Consider the production function y= . Assume r 1. (a) Show that the production function y(x) is concave. (b) Show that the inverse production function r(y) is convex (c) The price of y is p 10. Find the firm's total product TP(x), marginal product MP(a) and average product AP(a) (d) Find the firm's value of marginal product VMP(a), and value of average product VAP(r) (e) Assume w < marVAP (x) Find the firm's input demand curve r*(w) (f) Suppose...
Please write answer in fraction, and show all work. 1. Let P(L, K MRTS at the point (3, 5) 12L1/4K3/4 be a Cobb-Douglas production function. Find the Find the total differential, dP at (81, 16) if dL = 2 and dK = -.1 1. Let P(L, K MRTS at the point (3, 5) 12L1/4K3/4 be a Cobb-Douglas production function. Find the Find the total differential, dP at (81, 16) if dL = 2 and dK = -.1
3. Consider the production function y = x1. Assume r > 1. (a) Show that the production function y(x) is concave. (b) Show that the inverse production function (y) is convex. (c) The price of y is p = 10. Find the firm's total product TP(a), marginal product MPa) and average product AP(a). (d) Find the firm's value of marginal product VMPx), and value of average product V AP:). (e) Assume w<maxV AP(x) Find the firm's input demand curvex"(w). (1)...
3. DO NOT USE CALCULATOR for this problem! Find the EXACT VALUES for all the parts. Given the function f(x,y) (a) Calculate the total differential of z at the point (x, y, z) (b) Use the total differential to estimate the value of f(1+2(10200),-1 3(10-200). [ Hint : dz= 2(10-200) dy=_3(10-200)]. (c) Calculate the exact diffe ( f(1.-) I Note: total differentiala exact difference. ] rence of f(1+2(10-200)10 200))- (d) Find an equation for the plane s-L(x,y) tangent t(:-: f(z,y)...
Consider the production function given by y = f(L,K) = L^(1/2) K^(1/3) , where y is the output, L is the labour input, and K is the capital input. (a) Does this exhibit constant, increasing, or decreasing returns to scale? (b) Suppose that the firm employs 9 units of capital, and in the short-run, it cannot change this amount. Then what is the short-run production function? (c) Determine whether the short-run production function exhibits diminishing marginal product of labour. (d)...