ECON

posted by .

PLEASE CHECK AND CORRECT MY ANSWERS!!!!

MRTS = marginal rate of technical substitution
RTS = returns to scale
MP = marginal product

Suppose the production function is Cobb-Douglas and f(x1, x2) = [x1^(1/2)][x2^(3/2)]. (Note: x1 and x2 are variables).

a) Select an expression for MP of factor 1 at point (x1, x2).
b) MP of factor 1 ___ for small increases in x1, holding x2 fixed.
c) MP of factor 2 is _____ and it ____ for small increases in x2.
d) An increase in the amount of x2 _____ the MP of factor 1.
e) The technical rate of substitution between x2 and x1 is _____.
f) Does this technology have a diminishing technical rate of substitution?
g) This technology demonstrates ____ returns to scale.


My answers:
a) [x1^(-1/2)][x2^(3/2)]
b) increases
c) [3/2][x1^(1/2)][x2^(1/2)], decreases
d) increases
e) -(x2)/(3x1)
f) yes
g) decreasing

  • ECON -

    a) It should be (1/2)[x1^(-1/2)][x2^)3/2)

    b) I think decreases. Plug in an example. If x1 grows x1^(-1/2) gets smaller.
    c) the MP is correct. I think increases. Again, plug in an example. if x2 grows x2^(1/2) gets bigger.
    d) I agree
    e) i agree
    f) I agree
    g) I disagree. As the sum of the two exponents is > 1, this implies an increasing return to scale. Plug in an example. Increase x1 and x2 by some z percentage. Does output grow by more than z percent

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Managerial Economics

    I'm not sure I have the formulas correct for this problem and I do not know what the labor hours are.... Dimex Company, a sheet-metal mfg., estimates its long run production function is: 3 3 2 2 Q = -0.015625K L + 10K L where Q is …
  2. Economics

    Consider the production function Q = 20K 1/2 L 1/2. The firm operates in the short run with 100 units of capital. a. The firm’s short-run production function is Q = __________. c. The average product of labor function is AP = __________. …
  3. Economics Help pls

    Suppose you are given the following production function: , where y is output and K is capital. y= 60K + 20.3K2- K3 1.1 what is a production function, what is the real work application of such, and where would you source the data to …
  4. Economics

    Consider the production function Q= 20K^(1/2)L^(1/2). The firm operates in the short run with 16 units of capital. a. The firm's short-run production function is Q=?
  5. Algebra

    83. Minimizing Marginal Cost The marginal cost of a product can be thought of as the cost of producing one additional unit of output. For example, if the marginal cost of producing the 50th product is $6.20, it cost $6.20 to increase …
  6. micro

    hi, i need some help with my econ homework. i know what the law is, basically that more isn't always better. i just need to know how to tell if it applies to a labor equation. my problem goes like this. F(K,L) = K + 10L, write expressions …
  7. economics.Help!!!

    How the technical rate of substitution and marginal product are relates and what is their difference?
  8. microeconomics

    How the technical rate of substitution and marginal product are related and what is their difference?
  9. Macroeconomics help!

    Consider the following simplified economy described by a Cobb-Douglas production function with three factors of production: “K” is physical capital (the number of machines), “L” is labor (the number of workers), and “H” …
  10. Economics

    Consider the following simplified economy described by a Cobb-Douglas production function with three factors of production: “K” is physical capital (the number of machines), “L” is labor (the number of workers), and “H” …

More Similar Questions