Economics

posted by .

Please help me on this one!

You are planning to estimate a short-run production function for your firm, and you have the following data on labor usage and output:

Labor Output
3 1
7 2
9 3
11 5
17 8
17 10
20 15
24 18
26 22
28 21
30 23

A- Does a cubic equation appear to be a suitable specification, given these data? You may wish to construct a scatter diagram to help you answer this question.

B- Using a computer and software for regression analysis, estimate your firm short term production function using the data given here. Do the parameter estimates have appropriate algebraic signs? Are they statiscally significant at the 5 percent level?

C- At what point do you estimate marginal product begins to fall?

D- Calculate estimates of total, average, and marginal products when the firm employs 23 workers?

E- When the firm employs 23 workers, is short run marginal cost (SMC) rising or falling? How can you tell??

  • Economics -

    You still have two values of 17 labor with different outputs. That said, here goes.

    A) I wish there was more data, but a skatterplot kinda looks like an S-curve, which can be generated with a Cubic. So, yes.
    B) for y= ax + bx^2 + cx^3 + d
    I get (parameter and t-statistic):
    a=-.81426 (-1.30)
    b=0.10442 (2.46)
    c=.00183 (-2.17)
    d=2.9235 (1.14)

    Such parameters generate the shape shown in the skatter plot. With A cubic, its hard, a-priori to predict what the sign ought to be.
    Only b is significant at the 5% level
    C) the cubic is the total production function. Take the first dirivitive - this becomes the MP function. It has a maxima about 19. (check my math)
    D) Plug 23 into the estimated cubic function and the derived MP function
    E) since MP is falling at 23, SMC must be rising.

    I hope this helps

  • Economics -

    my bad, the parameter for c in my response should be -.00183

  • Economics -

    Hi,economyst. Can you please show me the step by step solution for D)


    thanks

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Economics

    You are planning to estimate a short-run production function for your firm, and you have collected the following data on labor usage and output. Labor usage output 3 1 7 2 9 3 11 5 17 8 17 10 20 15 24 18 26 22 28 21 30 23 (a) Does …
  2. managerial economics

    you are planning to estmate a short-run production for your firm, and you have collected the following data on labor usage and output: LABOR
  3. 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 = __________. …
  4. economics

    You are planning to estimate a short-run production function for your firm, and you have collected the following data on labor usage and output: Labor usage Output 3 1 7 2 9 3 11 5 17 8 17 10 20 15 24 18 26 22 28 21 30 23 Does a cubic …
  5. economics

    You are planning to estimate a short-run production function for your firm, and you have collected the following data on labor usage and output: Labor usage Output 3 1 7 2 9 3 11 5 17 8 17 10 20 15 24 18 26 22 28 21 30 23 Does a cubic …
  6. Economics

    Help me on this one please? labor usage -3,7,9,11,17,17,20,24,26,28,30 output-1,2,3,5,8,10,15,18,22,21,23 a. does a cubic equation appear to be a suitable specification, given these data?
  7. Economics

    Please Help You are planning to estimate a short-run production function for your firm, and you have collected the following data on labor usage and output: Labor Output 3 1 7 2 9 3 11 5 17 8 17 10 20 15 24 18 26 22 28 21 30 23 a.Does …
  8. economics

    You are planning to estimate a short-run production function for your firm, and you have collected the following data on labor usage and output: Labor Usage: 3 7 9 11 17 17 20 24 26 28 30 Output: 1 2 3 5 8 10 15 18 22 21 23 1) does …
  9. economics

    You are planning to estimate a short- run production function for your firm, and you have collected the following data on labor usage (L) and output (Q): Labor usage Output 3 1 7 2 9 3 11 5 17 8 17 10 20 15 24 18 26 22 28 21 30 23
  10. Managerial ECON

    You are planning to estimate a short- run production function for your firm, and you have collected the following data on labor usage (L) and output (Q): Labor usage Output 3 1 7 2 9 3 11 5 17 8 17 10 20 15 24 18 26 22 28 21 30 23 …

More Similar Questions