Problem 1

Suppose that the current market price of VCRs is $300, that average consumer disposable income is $30,000, and that the price of DVD players (a substitute for VCRs) is $500. Under these conditions annual U.S. demand for VCRs is 5 million per year. Statistical studies have shown that for VCRs the own-price elasticity of demand is –1.3. The income elasticity of demand for VCRs is 1.7. The cross-price elasticity of demand for VCRs with respect to DVDs is 0.8. Use this information to predict the annual number of VCRs sold under the following conditions:

1. Increasing competition from Asia causes VCR prices to fall to $270 with income and the price of DVDs is unchanged.
2. Income tax reductions raise average disposable personal income to $31,500
   with prices unchanged.
3. An inventor finds a cheaper way to produce DVDs, reducing the price of a DVD to $400, with the price of VCRs and income unchanged.
4. All of the events described in parts 1-3 occur simultaneously.

Problem 2

Chez Henri is a restaurant chain that operates in 40 different cities. It hired an economist to estimate the factors affecting
the demand for its sales. The following equation was estimated using cross sectional data from each of its 40 restaurants.

Y          Annual restaurant sales (in thousands)
X1        Disposable per capital income (in thousands) of the residents living within 5 miles of a restaurant
X2        Population (in thousands) within a 5 mile radius of a restaurant
X3        Number of competing restaurants within a 5 mile radius

The following information was obtained from the regression analysis

Multiple R               0.92
R-Square                0.85
Std. Error of Est.     0.40

Analysis of Variance

DF       Sum Squares     Mean Sqr.        F-Stat
Regression            3                220                  73.3               18.2
Residual               36                60                     1.7

Variable              Coefficient             Std. Error            T-Value
Constant                0.4                        0.2                       2.0
X1                         0.01                     0.004                    2.5
X2                         0.02                     0.015                    1.3
X3                       -20.2                     4.50                      -4.6

Answer the following questions:

1. Give the estimated demand equation for predicting restaurant sales.
   (b) Provide an interpretation for each of the regression coefficients.
   (c) Which of the coefficients are statistically significant and which are not? Explain.
   (d) What percent of variation is restaurant sales is explained by this equation?

Problem 3

Cameron is an investor trying to decide among the following three different investment options.

Option A:

Price today: $1000

One year from today Cameron will receive one of the following payments

$1,250 with a probability of 90%
$1,000 with a probability of 8%
$0 with a probability of 2%

Option B:

Price today: $1000

One year from today Cameron will receive one of the following payments

$4,000 with a probability of 30%
$1,000 with a probability of 50%
$0 with a probability of 20%

Option C:

Price today: $1000

One year from today Cameron will receive one of the following payments

$2,000 with a probability of 33%
$1,000 with a probability of 34%
$0 with a probability of 33%

a. What is the expected value (payment) of each of the options at the end of the year?

b. Which of the options has the highest risk? Why?

c. If Cameron is a risk neutral inventor, which option will be selected?

d. How would your answer change if Cameron is a risk averse investor?

Problem 4

The widget industry in Springfield is competitive, with numerous buyers and sellers.
Consumers don't differentiate among the various brands of widgets (no product differentiation).

The industry demand curve is given by:

Qd = 998 – 5Pw + 4 Y – 6Pg

And the industry supply curve is given by

Qs = +15Pw – 3 Wage

Where Pw represents the price of widgets, Pg is the price of gasoline, Y is disposable personal
income in Springfield, and Wage is wages paid to workers in widget factories.

Currently, Y= $10, Pg = $3, and Wage = $20.

a. Explain the meaning of the coefficients for each of the terms in the right hand side of the supply and
demand equations. Identify what the sign of each term indicates in terms of analyzing the equations.

b. Find the market equilibrium price and quantity using the information above.

c. Suppose Springfield’s economy moves into a recession and Y falls to $9 and rising unemployment
allows widget makers to reduce wages to $18 per hour. What happens to the supply and demand curves?
What can you predict will happen to equilibrium price and quantity?

d. Calculate the new equilibrium price and quantity.

.

Problem 5

Hernandez Corp. uses two variable inputs, X and Y, to produce its final product, canoes.

Its engineering department has estimated the marginal product functions for inputs X and Y
as follows:

MPx = Y/X

MPy = 4 X/Y

Where X and Y denote, respectively, the quantity in hours of inputs X and Y used.

At present Hernandez Corp. pays $40 per hour for input X and $10 per hour for input Y.
It is using 200 hours of X and 100 hours of Y per day.

a. Write a paragraph explaining how the Hernandez Corp. finds the least cost combination
of inputs for producing a given rate of output.

b. Using the data provided above, determine if the Hernandez Corp. is using a cost minimizing
combination of inputs. Explain your answer/show your work. If your answer is no, how should
the input combination be adjusted.

Price: $23.95

Solution: The downloadable solution consists of 8 pages, 1595 words and 3 charts.
Deliverable: Word Document