1.(13 points) The following table shows the number of calculators that
can be assembled per week by various numbers of workers.

a.(5) Fill in the missing numbers in the table.
Show all your calculations.

b.(8) 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.(39
points) 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 = 0.81R²
= 0.782F = 28.42SEE
= 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.(5) 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. (5) 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.(10) 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.(8) 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.(3) 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.(8) 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. (15 points)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.(3) What is
the price elasticity of demand for tours? Interpret your answer. Given this
elasticity, should Breakaway increase prices to increase revenue? Explain.

b.(3) Are tours a normal good? Explain.

c.(3) What is the
relationship between Goods X and Y? How strong is this relationship? Explain
each answer well.

d.(3) Does advertising seem
effective for this company? Explain.

e.(3) 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.(23 points) 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:

a.(8) Construct a table
showing the (net) marginal revenue product derived from assembly worker
employment.

b.(10) How many assemblers
would Just Bikes employ at a daily wage rate of $100? Explain your answer and
show all calculations.

c.(5) What is the highest
daily wage rate Just Bikes would pay to hire three assemblers per day?

5.(10 points) 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)?

Attachments:

APS2-T4-13.doc