Download Econ 201 Lecture 11 Example 11.1. How should Leroy divide his

Econ 201 Lecture 11
Example 11.1. How should Leroy divide his time between picking apples and writing pulp fiction?
A men's magazine will pay Leroy 10 cents per word to write fiction articles. He must decide how to divide his time
between writing fiction, which he can do at a constant rate of 200 words per hour, and harvesting apples from the trees
growing on his land, a task only he can perform. His return from harvesting apples depends on both the price of apples and
the quantity of them he harvests. Earnings aside, Leroy is indifferent between the two tasks. The amount of apples he can
harvest depends, as shown in the table below, on the number of hours he devotes to this activity:
Hours
Total bushels
1
8
2
12
3
15
4
17
5
18
Additional bushels
8
4
3
2
1
For each hour Leroy spends picking apples, he loses the $20 he could have earned writing pulp fiction.
He should thus spend an additional hour picking as long as he will add at least $20 worth of apples to his total
harvest.
For example, if apples sell for $2.50 per bushel, Leroy would earn $20 for the first hour he spent picking apples, but
would earn only an additional $10 if he spent a second hour. Thus, at a price of $2.50 per bushel, Leroy would allocate 1
hour to picking apples, during which time he will harvest 8 bushels.
If the price of apples then rose to $5 per bushel, it would pay Leroy to devote a second hour to picking, which
would mean a total of 12 bushels of apples. Once the price of apples reached $6.67 per bushel, he would devote a third hour
to picking apples, for a total of 15 bushels. If the price rose to $10 per bushel, he would pick for four hours and get 17
bushels. And, finally, once the price of apples reached $20 per bushel, Leroy would supply five hours of apple-picking
services, and would harvest 18 bushels of apples.
Leroy's individual supply curve for apples relates the amount of apples he is willing to supply at various prices.
Hours
Total bushels
1
8
2
12
3
15
4
17
5
18
Additional bushels
8
4
3
2
1
P ($/bu)
Leroy's supply curve
for apples
20.00
10.00
6.67
5.00
2.50
8
12 15
18
17
Q (bu/day)
An Individual Supply Curve for Apples
2
Market Supply
The quantity that corresponds to any given price on the market supply curve is the sum of the quantities supplied at
that price by all individual sellers in the market.
Example 11.2. If the supply side of the apple market consisted of 100 suppliers just like Leroy, what would the market
supply curve for apples look like?
P ($/bu)
Market supply curve
for apples
20.00
10.00
6.67
5.00
2.50
8
12 15
18
17
Q (100s of bu/day)
The Market Supply Curve for Apples
As noted earlier, the typical individual supply curve is upward sloping, at least in the short run, for two reasons:
1. The Fruit Picker's Rule (Always pick the low-hanging fruit first).
When fruit prices are low, it might pay to harvest the low-hanging fruit but not the fruit growing higher up the tree,
which takes more effort to get to.
But if fruit prices rise sufficiently, it will pay to harvest not only the low-hanging fruit, but also the fruit on higher
branches.
2. Differences among suppliers in opportunity cost
People facing unattractive employment opportunities in other occupations may be willing to pick apples even when
the price of apples is low. Those with more attractive options will pick apples only if the price of apples is relatively high.
Profit-Maximizing Firms and Perfectly Competitive Markets
Definition. The profit earned by a firm is the total revenue it receives from the sale of its product minus all costs—explicit
and implicit—incurred in producing it.
Definition. A profit-maximizing firm is one whose primary goal is to maximize the difference between its total revenues
and total costs.
Definition. A perfectly competitive market is one in which no individual supplier has significant influence on the market
price of the product.
Wheat Market
Photocopying Market
Definition. A price taker is a firm that has no influence over the price at which it sells its product.
Wheat farmers, Kinko’s.
Contrast with price setter: Microsoft operating systems, Intel microprocessors
Definition. A factor of production is an input used in the production of a good or service.
Definition. A fixed factor of production is an input whose quantity cannot be altered in the short run.
Definition. A variable factor of production is an input whose quantity can be altered in the short run.
Example. Louisville Slugger uses two inputs, labor (e.g., woodworkers) and capital (e.g., lathes, tools, buildings), to
transform raw materials (e.g., lumber) into output (baseball bats). Labor is a variable input and capital is a fixed input.
Total number of employees per day
0
1
2
3
4
5
6
7
Total number of bats per day
0
40
100
130
150
165
175
181
3
Note in the right column that output gains begin to diminish with the third employee. Economists refer to this
pattern as the law of diminishing returns, and it always refers to situations in which at least some factors of production are
fixed.
Here, the fixed factor is the lathe, and the variable factor is labor.
Some Important Cost Concepts
Suppose the lease payment for the Louisville Slugger’s lathe and factory is $80 per day. This payment is both a
fixed cost (since it does not depend on the number of bats per day the firm makes) and, for the duration of the lease, a sunk
cost.
The company’s payment to its employees is called variable cost, because unlike fixed cost, it varies with the
number of bats the company produces. The firm’s total cost is the sum of its fixed and variable costs. The firm’s marginal
cost, finally, is the change in total cost divided by the corresponding change in output.
Louisville slugger pays each employee a wage of $24/day.
Example 11.3. For each level of employment, calculate Louisville Slugger’s output, fixed cost, variable cost, total cost and
marginal cost.
Employees
per day
Bats per
day
Fixed cost
($/day)
Total cost
($/day)
80
Variable
cost
($/day)
0
0
0
1
40
80
24
104
2
100
80
48
128
3
130
80
72
152
4
150
80
96
176
5
165
80
120
200
6
175
80
144
224
7
181
80
168
248
Marginal
cost
($/bat)
80
0.60
0.40
0.80
1.20
1.60
2.40
4.00
Choosing Output to Maximize Profit
If a company’s goal is to maximize its profit, it should continue to expand its output as long as the marginal benefit
from expanding is at least as great as the marginal cost.
Example 11.4. Suppose the wholesale price of each bat (net of lumber and other materials costs) is $2.50. How many bats
should Louisville Slugger produce?
If we compare this marginal benefit ($2.50 per bat) with the marginal cost entries shown in table, we see that the firm should
keep expanding until it reaches 175 bats per day (6 employees per day).
To confirm that the cost-benefit principle thus applied identifies the profit-maximizing number of bottles to
produce, we can calculate profit levels directly:
Employees per day
0
1
2
3
4
5
6
7
Output
(bats/day)
0
40
100
130
150
165
175
181
Total revenue
($/day)
0
100
250
325
375
412.50
437.50
452.50
Again note that 6 employees corresponds to the maximum-profit level of output.
Total cost
($/day)
80
104
128
152
176
200
224
248
Profit
($/day)
-80
-4
122
173
199
212.50
213.50
204.50
4
When the law of diminishing returns applies (that is, when some factors of production are fixed), marginal cost goes up as
the firm expands production beyond some point. Under these circumstances, the firm's best option is to keep expanding
output as long as marginal cost is less than price.
Note in Example 11.4 that if the company's fixed cost had been any more than $293.50 per day, it would have made
a loss at every possible level of output. As long as it still had to pay its fixed cost, however, its best bet would have been to
continue producing 175 bats per day, because a smaller loss is better than a larger one.
If a firm in that situation expected conditions to remain the same, it would want to get out of the bat business as
soon as its equipment lease expired.