8. Explain how three of the most common production functions (Linear, Cobb Douglas and Leontief) are particular cases of the Constant Elasticity of Substitution production function.
8. Explain how three of the most common production functions (Linear, Cobb Douglas and Leontief) are...
For all the utility functions (CES, Cobb-Douglas, quasi-linear, linear, Stone-Geary and Leontief) in the attached document, formally derive the Marshallian demand functions and the related expenditure functions.
explain what is meant by the issue of a Cobb-Douglas production being similar to a recipe with no steps. How does the Leontief production function deal with this problem? Give a real world example! (Hint: think about the output of an jazz band that produces music, where the inputs are the number of musicians - labor - and the number of instruments - capital.)
An economy has a Cobb Douglas production function, given by: a, (1-a) (1) YAK L Where Yis equal to total production, K is equal to the capital input of production and L is equal to the labour input of production. The constant, A, represents technology in the economy and a the elasticity of capital. function exhibits, decreasing, increasing or constant returns to scale. [ 10 Marks A2. Carefully derive the marginal product of labour and explain how this might be...
Question-3 (Marginal Products and Returns to Scale) (30 points)
Suppose the production function is Cobb-Douglas and f(x1; x2) =
x1^1/2 x2^3/2
1. Write an expression for the marginal product of x1.
2. Does marginal product of x1 increase for small increases in
x1, holding x2 fixed? Explain
3. Does an increase in the amount of x2 lead to decrease in the
marginal product of x1? Explain
4. What is the technical rate of substitution between x2 and
x1?
5. What...
8 Find the marginal-product functions for the Cobb-Douglas production func- tion for i 1, 2, 3, 4 a2a3a4 y Axixx3x4 A> 0, 0< ai <1
Please help with part c. Thank you!Returns to scale Consider the Cobb-Douglas production function, Yt = KẠN L-a=b. This production function includes three inputs: capital (Kt), labor (Nt), and land (Lt). a) Under what conditions does the function exhibit decreasing returns to scale in Kt, Nt and Lt individually? b) Show that the function exhibits constant returns to scale in Kt, Nt and Ljointly. c) Define (lowercase) yt = *, ku = and lt = . Express Yt as a...
A “Cobb–Douglas” production function relates production (Q) to factors of production, capital (K), labor (L), and raw materials (M), and an error term u using the equation: ? = ???1??2M?3? ?, where ?, ?1, ?2, and ?3 are production parameters. a) Suppose that you have data on production and the factors of production from a random sample of firms with the same Cobb–Douglas production function. How would you propose to use OLS regression analysis to estimate the above production parameters,...
2. For the following Cobb-Douglas production function, q = f(L,K) = _0.45 0.7 a. Derive expressions for marginal product of labor and marginal product of capital, MP, and MPK. b. Derive the expression for marginal rate of technical substitution, MRTS. C. Does this production function display constant, increasing, or decreasing returns to scale? Why? d. By how much would output increase if the firm increased each input by 50%?
8. Find the marginal-product functions for the Cobb-Douglas production func- tion y = A.X. XXX A>0,0<«; <1 for i = 1, 2, 3, 4
Suppose the production function is Cobb-Douglas and f(x1, x2) =
x^1/2 x^3/2
(e) What's the technical rate of substitution TRS (11, 12)? (f) Does this technology have diminishing technical rate of substitution? (g) Does this technology demonstrate increasing, constant or decreasing returns to scale?