Try to work these on your own, but feel free to discuss
these with other students, Nazmi or me if you want.
1. Add or subtract the following linear functions:
- Y = 2 + 4X plus Y = 4 + 2X
- Q = 5 - 2P plus Q = -2 + 0.5P
- TR = 10Y minus VC = 0.05Y^2 minus FC = 20
2. Between 2000 and 2003 the price of a small pizza increased from
$5.00 to $6.00, and the price of a liter of soda stayed the same at $1.25.
- In 2000, Filbert consumed 5 pizzas and 10 liters of soda per week.
Using 2000 as the base year, calculate the cost index for Filbert's
2000 consumption bundle in 2003.
- In 2003, Filbert (who still hasn't graduated) is actually consuming
4 pizzas and 13 liters of soda per week. Using 2000 as the base year,
calculate the cost index for Filbert's 2003 consumption bundle.
3. Invert the following equations (solve for the right-hand side variable
in terms of the left-hand side variable):
- Q = 100 - 0.25P
- Y = 32.6 + 0.54X
- MC = -10 + 0.05Y^2
4. If a monopolist is selling in a market with demand Q = 64
- 2P, calculate the price elasticity of demand and the monopolist's total
revenue (P x Q) where...
- Q = 20
- Q = 30
- Q = 40
- Q = 50
5. Solve the following supply-demand equations to determine the market
equilibrium point:
- Q(demand) = 200 - 0.25P Q(supply) = P - 25
- Q(demand) = 16.7 - 0.0012P P = 0.05Q(supply) + 2
6. You are using a spreadsheet to model a single-input producer, and
have the following spreadsheet fragment:
| A | B
| C
------------------------
1 |P(X)= P(Y)= FC=
2 | $7.00 $4.50 $50.00
3 |
4 | X
Y
5 | 0
0
6 | 1
2
7 | 2
5
What spreadsheet formulas would you enter in Row 6 for each of the following?
- (column C) MPP
- (column D) APP
- (column E) MVP
- (column F) MFC
- (column G) TR
- (column H) VC
|
- (column I) TC
- (column J) ATC
- (column K) MC
- (column L) MR
- (column M) Profit
|
- How will an increase in P(X) affect the profit-maximizing levels of
X and Y? Explain.
- How will an increase in P(Y) affect the profit-maximizing levels of
X and Y? Explain.
- How will an increase in FC affect the profit-maximizing levels of X
and Y? Explain.
7. Suppose you used a really primitive regression package to regress
quantity of chicken demanded (Q) against price per pound (P), and obtained
the following regression output. The model being tested is Q = a +
bP, and the hypothesis for coefficient b is that b<0.
SUMMARY OUTPUT
R Square 0.425
Observations 21
Coeffs StdError
Intercept 17.12 6.40
P (price) -0.64 0.41
- Calculate the t-statistics for the Intercept and Price coefficients
(divide the coefficient value by the StdError).
- Analyze the statistical significance of each coefficient based on its
t-statistic. How well does this model support the hypothesis that b<0?
More formally, does this model REJECT the null hypothesis that b is NOT negative
at the 95% or better confidence level?
- What percent of the total variation in quantity demanded is explained
by this model?
- If it takes two observation points to even define the line (slope and
intercept), how many additional observation points ("degrees of freedom")
are contributing residual variation that lets us compute statistical significance?
- Calculate the point elasticity of demand where Q = 10.
8. Suppose you regressed quantity of golf balls demanded against the
price of golf balls, greens fees, price of tennis rackets and income:
Q(golfballls) = a + b1*P(golfballs) + b2*P(greensfees) + b3*P(tennisrackets)
+ b4*Income.
What signs would you expect for each of the b coefficients? Explain.
9. When an economist refers to children as "inferior goods," what does
she mean? When she calls health care a "luxury good," what does she
mean?
10. If a firm's total profit function is PROFIT = -100 + Y - 0.001Y^2,
- What is its MARGINAL profit function (the derivative of the total profit
function)?
- Solve this marginal profit function for the output level Y where marginal
profit equals zero.
- What is the firm's total profit at the output level where marginal
profit equals zero? Explain why this output level yields the maximum
TOTAL profit.