Reference no: EM13375564

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:

                        Q_A =     445   -             6.5P_A    +   0.75P_B   +   1.85Y

                      (1.4)          (0.35)          (0.95)              (standard errors)

                                               _

          R² = 0.81                                   R² = 0.782                   F = 28.42                     SEE = 5.25                  

 

where         Q_A        =          quantity sold per month of good A, in units

                  P_A        =          price of good A, in US$

                  P_B        =          price of good B, in US$

                  Y         =          average income, in thousands US$

a. Interpret the estimated coefficients of P_A, Y and P_B. 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. Do not use rules of thumb.

3. Breakaway Tours, Inc., has estimated the following multiplicative demand function for packaged holiday tours in the Flushing, New York, market using quarterly data covering the past five years (20 observations):

          Q_Y = 5P_Y^-2.5P_X^-0.86Y^1.76A^1.4

Here, Q_Y is the quantity of tours sold, P_Y is average tour price, P_X is average price for some other good, A is tour advertising, and Y is per capita disposable income.

a. What is the price elasticity of demand for tours? Interpret your answer. Given this elasticity, should Breakaway increase prices to increase revenue? Explain.

b. Are tours a normal good? Explain.

c. What is the relationship between Goods X and Y? How strong is this relationship? Explain each answer well.

d. Does advertising seem effective for this company? Explain.

e. What does the demand function above suggest about the relationship of each variable to each other? Does elasticity ever change if the values of P_Y, P_X, Y, or A change? Explain.

4. Just Bikes, Inc., sells tricycles, in partially-assembled and fully assembled forms. Parents who assemble their own tricycles benefit from the lower price of $40 per tricycle. "Full-service" customers enjoy the luxury of an assembled tricycle, but pay a higher price of $60 per tricycle. Both partially and fully assembled tricycle prices are stable. The company has observed the following relation between the number of assembly workers employed per day and assembled tricycle output:

Number of Workers per day	Finished Tricycles
0	0
1	8
2	14
3	18
4	21
5	23

a. Construct a table showing the (net) marginal revenue product derived from assembly worker employment.

b. How many assemblers would Just Bikes employ at a daily wage rate of $100? Explain your answer and show all calculations.

c. What is the highest daily wage rate Just Bikes would pay to hire three assemblers per day?

5. Describe the difference between a diminishing marginal product of labor and a negative marginal product of labor. Why would a profit-maximizing firm always choose to operate where the marginal product of labor is decreasing (but not negative)?