1. The following table shows the number of calculators that can be assembled per week by various numbers of workers.
|
Quantity of
|
Number of Calculators
|
Average
|
Marginal
|
|
Labor
|
Per Week
|
Product
|
Product
|
|
0
|
0
|
--
|
--
|
|
1
|
|
60
|
|
|
2
|
160
|
|
100
|
|
3
|
|
|
80
|
|
4
|
280
|
|
|
|
5
|
|
60
|
|
a. Fill in the missing numbers in the table. Show all your calculations.
b. Identify the level of output above where the firm is in Stage II of production. Why will the rational producer never operate in Stages I or III? Explain your answers well.
2. Using linear regression and 24 months of data, a firm estimated its demand function for its Good A and achieved the following results:
QA = 445 - 6.5PA + 0.75PB + 1.85Y
(1.4) (0.35) (0.95) (standard errors)
R2 = 0.81 R'2 = 0.782 F = 28.42 SEE = 5.25
where QA = quantity sold per month of good A, in units
PA = price of good A, in US$
PB = price of good B, in US$
Y = average income, in thousands US$
a. Interpret the estimated coefficients of PA, Y and PB. In other words, how much a one unit change in each variable influence sales of Good A? Be specific (use numbers).
b. Evaluate the overall explanatory power of the regression model. Use a 0.05 level of significance. State all your hypotheses and explain your results. Do not use rules of thumb.
c. Which of the independent variables, if any, appear to be statistically significant at the 0.05 level in explaining sales? State all your hypotheses and explain your results. Do not use rules of thumb.
d. At present, the price of Good A is $40, the price of Good B is $65, and average income is $40,000 (be careful of units used in the equation for this variable!). Calculate the price, cross-price, and income elasticities of demand at present. Interpret each elasticity and say what each tells you about how much a 1% change in each impacts the quantity demanded in percent.
e. What proportion of the total variation in sales is explained by the independent variables in this regression equation? Is the answer influenced significantly by the size of n relative to k? Explain.
f. Derive a 95% confidence interval for current sales at the present values of each variable given in part D.