EC155A and B
October 20, 2002
Take-home exercise 1
- Using the data that we reviewed in class on Friday (see the table below), discuss why one can determine the profit maximizing point from only the data in the ‘Marginal Costs’ column. What is the profit maximizing amount of sign production?
|
The
Short-term Production and Costs of Midd Signs |
|
|
|
|
|
|
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
PRODUCTION |
COSTS |
BOTTOM LINE |
|||||||||
|
INPUT (labor) |
OUTPUT (signs) |
MARGINAL PRODUCT |
FIXED COSTS (FC) |
VARIABLE COSTS (VC) |
TOTAL COSTS (TC) |
MARGINAL COSTS (MC) |
AVERAGE FIXED COSTS (AFC) |
AVERAGE VARIABLE COSTS (AVC) |
AVERAGE TOTAL COSTS (ATC) |
REVENUE |
PROFIT |
|
L |
Q=f(L,X) |
MP = ΔQ/ΔL |
Costs of X |
VC = W*L |
TC = FC+VC |
MC = ΔTC/ΔQ |
AFC = FC/Q |
AVC = VC/Q |
ATC = TC/Q |
R = P*Q |
Π=P*Q – TC |
|
1 |
4 |
4 |
$20.00 |
$15.00 |
$35.00 |
|
$5.00 |
$3.75 |
$8.75 |
$40.00 |
$5.00 |
|
2 |
9 |
5 |
$20.00 |
$30.00 |
$50.00 |
$3.00 |
$2.22 |
$3.33 |
$5.56 |
$90.00 |
$40.00 |
|
3 |
13 |
4 |
$20.00 |
$45.00 |
$65.00 |
$3.75 |
$1.54 |
$3.46 |
$5.00 |
$130.00 |
$65.00 |
|
4 |
16 |
3 |
$20.00 |
$60.00 |
$80.00 |
$5.00 |
$1.25 |
$3.75 |
$5.00 |
$160.00 |
$80.00 |
|
5 |
18 |
2 |
$20.00 |
$75.00 |
$95.00 |
$7.50 |
$1.11 |
$4.17 |
$5.28 |
$180.00 |
$85.00 |
|
6 |
19 |
1 |
$20.00 |
$90.00 |
$110.00 |
$15.00 |
$1.05 |
$4.74 |
$5.79 |
$190.00 |
$80.00 |
|
7 |
18 |
-1 |
$20.00 |
$105.00 |
$125.00 |
-$15.00 |
$1.11 |
$5.83 |
$6.94 |
$180.00 |
$55.00 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
The
price of a Midd Sign: |
|
|
$10.00 |
|
|
|
|
|
||
|
|
Wage
rate: |
|
|
|
$15.00 |
|
|
|
|
|
|
|
|
Fixed
cost of materials (paper, staples, pen): |
|
$20.00 |
|
|
|
|
|
|||
It must be with an output of 18 (which is an input of 5): this is where MB ($10) > MC ($7.50). At an output of 19, by contrast MB ($10) > MC ($15.00).
- Confirm your answer by filling in the last two columns of the table.
See figures above
- What would be the profit maximizing amount of sign production if the fixed cost were $40? What would be the profit maximizing amount of sign production if the fixed cost were $120? Justify your answers.
They would be the same, since
the MB > MC rule would still hold there.
A change in fixed costs do not affect marginal costs. (You can check this by looking at the profit
figures in the last column, after using the new fixed costs.)
- With ‘cost per unit’ on the vertical axis and ‘quantity of signs’ on the horizontal axis, plot the AFC, AVC, ATC, and MC curves, using the data in the table.
PROFITS P = $10
- Using the table and/or the graph, explain why:
a) The AFC is always falling;
b) The AVC first falls and then rises;
c) The ATC first falls and then rises;
d) MC first falls and then rises.
See the descriptions in Colander (pp. 208 – 213) about the shapes of these curves.
- Plot the price of $10 on the same graph. Can you find the area that represents profits? [HINT: Profit = Revenue – Costs = P*Q – ATC*Q.]
See the rectangle on the graph.