FREC 834 -- intro
theory review/skills assessment
1. Sketch a 3x4 array of little demand curve diagrams
for (1) coffee, (2) powdered creamer, a complement to coffee, and (3)
tea, a substitute for coffee, with respect to (a) the price of coffee,
(b) the price of creamer, (c) the price of tea, and (d) income, where
coffee is normal, powdered creamer is inferior, and tea is a
luxury. Show the effects in all 12 graphs of an increase in the
price of creamer.
2. Suppose a competitive firm produces output Y with
the following cost structure:
Output Y
|
AVC
|
ATC
|
MC
|
| 1 |
$ 5.00 |
$ 15.00 |
$ 4.00
|
| 3 |
$
3.33 |
$ 6.67 |
$ 2.50 |
| 6 |
$ 2.50 |
$ 4.17 |
$
1.67 |
| 10 |
$ 2.00 |
$ 3.00
|
$ 1.25 |
| 15 |
$
1.67 |
$ 2.33 |
$ 1.00 |
| 19 |
$
1.58 |
$ 2.15 |
$ 1.58 |
| 22 |
$ 1.65 |
$ 2.10 |
$ 2.10 |
| 24 |
$ 1.80 |
$ 2.22 |
$ 3.00 |
| 25 |
$ 2.00 |
$ 2.40
|
$ 5.00 |
- At a competitive market price of $3 per unit of Y, how much would
the firm produce, and what would its profit be?
- At what market price of Y would the firm just break even, and how
much would it produce at that price?
- At what market price of Y would the firm shut down in the short
run?
- Calculate the arc elasticity of the firm's supply schedule
between 19 and 22 units of output.
3. If the market supply and demand for widgets are Qs
= -200 + P and Qd = 400 - 0.5P respectively,...
- Calculate the market equilibrium P and Q.
- Calculate the point elasticities of supply and demand at
equilibrium.
- Calculate the consumer and producer surpluses.
- If the government imposes a tax of $30 per unit on widgets,
calculate the new equilibrium quantity, consumer and producer surpluses
and deadweight loss.
4. Basic applications of derivatives:
- If a competitive firm's average total cost = 1.5Q + 4 + 54/Q,
what is its marginal cost function? What is its break-even market
price?
- If Profit = - Q3 - 6Q2 + 1440Q - 525, what
is the profit-maximizing level of Q? Prove this isn't the profit-minimizing point.
5. If A = [ a b ], calculate...
- A'
- A'A
- AA'
- |A'A|
- (A'A)-1
6. A regression analysis yields the empirical demand model
with coefficient standard errors in parentheses:
Quantity
= 16.25 - 0.463*Price + 0.00051*Income
(2.05) (0.096)
(0.00040)
N = 126; R-square = 0.45
Give a brief interpretation of these results.