Quiz on Production Theory and Estimation E303 Spring 02

1. Which of these must happen if there are diminishing marginal returns to an input?

A. the production function eventually declines

B. the marginal product eventually declines

C. the marginal product eventually becomes negative

D. all inputs are eventually decreased

2. Which of the following best defines the "marginal revenue product" in words?

A. the extra product when you increase one input by a unit holding others constant

B. the extra product, valued at its market price, when you increase one input by a unit holding others constant

C. the extra product you can purchase with one extra dollar of money

D. the extra money you can earn by selling one unit of product

3. Find the expression for the marginal rate of technical substitution for a production function Q = AK.7L.3 (you can assume that K is on the vertical axis).

A. AK.7L.3

B. -K/L

C. -.3K/.7L

D. - .7K/.3L

E. -AKL

4. Define "decreasing returns to scale".

A. when increasing an input holding others constant, the marginal product eventually declines

B. when decreasing output by 10% the revenue decreases by less than 10%

C. when increasing each input by 10% the output increases by more than 10%.

D. when increasing each input by 10% the output increases but by less than 10%

E. when increasing each input by 10% the output decreases by 10%.

5. For the Cobb Douglas production function, Q = 100K.4L6 , assume that the input prices for capital and labor are r=20 and w=10. If you are required to employ L=60 workers and are given the necessary production budget, what is the allocatively efficient quantity of capital, K, to use?

A. K=100

B. K=20

C. K=40

D. K=16

E. K=60

For the next question, fill in the blanks in the following table and insert the correct response on you Scantron. Notice that "marginals" are defined in this case using the practical assumption that the change in labor is one whole unit.

Amount of labor / Output of parts / Average product / Marginal product
0 / 0 / - / -
1 / 49 / 49 / 49
2 / 132 / 66 / 83
3 / 243 / 81 / missing marg. prod.
4 / 376 / missing ave product / 133

6. The missing average product and the missing marginal product in the above table are

A. 94 and 111

B. 90 and 83

C. 34 and 49

D. 94 and 120

E. 98 and 132

7. Let the production function for your product be Q = 120 + 20L - .21L2. Assume that laborers are paid a wage of $30 and that your product sells for $45. Approximately how many laborers should you hire?

A. 120

B. 32

C. 12

D. 46

E. 104

8. Which of the following best defines an isoquant? (You can assume that we are defining it in the context of the K by L quadrant).

A. a collection of all points where the marginal product of labor is the same

B. a collection of all points where the marginal rate of technical substitution is the same

C. a collection of all points where the output is the same

D. a collection of all points where the profit is the same

E. a collection of all points where the quantity of labor is the same

9. The equation such as (Q/K)/r = (Q/L)/w, is a condition of production required to achieve which of the following?

A. allocative efficiency

B. profitable production

C. pricing below your competitor

D. just in time production

E. modern design

The following four questions pertain to the summary output table below, which can be assumed to come from a regression of a the log/log version of a Cobb-Douglas production function estimated over five input variables.

Summary Output

REGRESSION / STATISTICS
Adj R Squared / 0.895
Observations / 36
ANOVA / df / F / Signif
Regressors / 5 / 60.81 / 8.61E-15
Residual / 30
REGRESSION / Coeffs. / Stnd Error / t statistics
Intercept / 5.943 / 0.237 / 25.04
ln Skilled labor / 0.143 / 0.019 / 7.44
ln Unskilled L / 0.007 / 0.035 / 0.21
ln Equipment / 0.028 / 0.017 / 1.62
ln Materials / 0.328 / 0.023 / 14.21
ln Other inputs / 0.003 / 0.025 / 0.12

10. Which statistic tests the hypothesis that the true mean values for all five input regression coefficients are zeroes, and which does the reported data imply is true regarding that hypothesis, that it should be rejected or accepted?

A. R square, and the hypothesis is accepted

B. F statistic, and the hypothesis is accepted

C. t statistic, and the hypothesis is accepted

D. R square, and the hypothesis is rejected

E. F statistic, and the hypothesis is rejected

11. Which of the regression coefficients contributes significantly to production of this output using the usual two-tailed test of significance?

A. Skilled labor, Unskilled labor, and Materials

B. Skilled labor and Materials

C. Skilled labor, Equipment, and Materials

D. Equipment and Other inputs

E. none of the above

12. Which statistic measures "goodness of fit," and by our usual rules of thumb would you say that this is equation is a good fit or a poor fit?

A. F statistic, and this is a poor fit

B. R squared statistics, and this is a poor fit

C. t statistic, and this is a poor fit

D. R squared statistic, and this is a good fit

E. t statistic and this is a good fit

13. Find the "output elasticity" in this estimated equation:

A. 0.51

B. 1.23

C. 1.00

D. 0.78

E. 3.89

14. Considering a pair of inputs, capital and labor, suppose that presently the ratios of marginal product to input price were '34 widgits per dollar for capital' and '22 widgits per dollar for labor'. Which of the following can you logically conclude?

A. capital is being overutilized compared to labor

B. labor is being overutilized compared to capital

C. the firm has achieved allocative efficiency

D. the firm should hire more of both inputs

E. none of the above

15. The statistic "Adjusted R squared", we have said, adjusts the initially calculated R squared for some possibly misleading difference of the study at hand from the typical study. What is it that Adjusted R squared adjusts for?

A. erroneous t statistics

B. differences in degrees of freedom

C. too many independent variables

D. values that are lost due to rounding