Chapter 6 Perfectly Competitive Supply: The cost side of the market

Chapter 6
Perfectly Competitive Supply:
The cost side of the market
Even-numbered Qs. and #3 #9
4 additional questions
• Profit-maximizing firm
- Goal is to maximize profit,
- Profit = Total Revenue – Total Cost
- Total costs include explicit and implicit costs
• Perfectly Competitive Market
- Firms in this market make many decisions; but one thing they do not
decide is the price at which to sell their output
- Firms in perfect competition are said to be price taker
- Price taker – a firm that cannot influence the price of a good or service
- At the market price, individual firm can sell as much or as little quantity
as it wishes
- Individual firm’s demand curve is perfectly elastic
• Five conditions of Perfectly competitive market:
1)
All firms are price-taker
2)
All firms sell the same standardized product to many buyers
- buyers are able to switch from one seller to another if the price of the good is
lower
- substitution goods are available
3)
The market has many buyers and sellers, they have a relatively small
market share of the total quantity exchanged
- individual’s decision will have no impact on the market price
4)
Productive resources are mobile
- free to enter or exit the market
5)
Buyers and sellers are well informed about product being sold and the
prices charged by each firm
- Buyers are able to seek for the lowest price
- Sellers are able to seek for the “most-profit earning” opportunities
• Factors of Production:
- inputs used in production
- it can be variable or fixed
• Variable factor of production
- input can be varied in the short run
- i.e. labor – firms can increase production simply by having labors working
overtime in a short notice
• Fixed factor of production
- input cannot be varied in the short run
- i.e. machinery, a factory – it takes time to install a new equipment, train
labors to use it; and it takes time to plan and build a new factory
• Short run vs. Long run
• Short run
- at least one input is fixed and the other inputs are variable
- it is impossible to add another factory or install a machine in
a short period of time
• Long run
- all inputs are variable
- it is sufficient to add another factory or install a machine in a
long period of time
• The short run and long run distinction varies from one
industry to another
• Law of Diminishing Returns
• - as adding more variable inputs, the marginal production grows,
(increasing marginal returns); but beyond some point, the marginal
production starts to diminish (decreasing marginal returns)
• - it only applies to the short run, at least one input is fixed and the other
inputs can be varied
• Marginal Product: the change in total product/the change in variable input
- i.e., a firm hires some additional labors in the car production and the
amount of machinery stays the same, then, the used of the machine
would be overcrowded. The marginal productivity grows only for the first
few units of labors, then it starts to diminish. Therefore, marginal
productivity actually decreases
• Marginal Cost: the change in total cost (total variable cost)/the change in
quantity
- MC at first decreases sharply, it reaches a min. point, then again, starts to
increase
- This reflects the fact that VC, or TC increases by a decreasing amount and
then TC increases by an increasing amount
- The shape of the MC curve is a consequence of the Law of Diminishing
Return
MC
MC
Law of diminishing returns
Quantity
• Law of Diminishing Returns
• it only applies to the short run, at least one input is fixed and
the other inputs can be varied
• In the Short run, MC curve is U-shape
• in the Long run, MC curve is horizontal
• in the long run, all inputs are variable. The firm can often
double its production by simply doubling the amount of each
input they use
• Thus, cost is proportional to output
• Therefore, MC in the long run is horizontal, not upward
sloping
• For a perfectly competitive firm, it chooses to produce at a
point where P=MC
• If P > MC: Firm can increase its profit by increasing output
• If P < MC: Firm can increase its profit by decreasing output
Firms earn profit
P > ATC where Q is at optimal level of output
Firms suffer loss
P < ATC where Q is at optimal level of output
Firms break-even, TR = TC,
earning zero Economic profit
P = ATC where Q is at optimal level of output
Firms shutdown point
P = min. AVC
Firms should shutdown
P < min. AVC, loss = fixed cost
To Summarize:
• If P > ATC > min. AVC
Firms earn profit and stay in the market
• If ATC > P > min. AVC
Firms suffer loss but continue to operate
• If ATC > min. AVC > P
Firms should shutdown and loss equals to its fixed cost
Additional Question #1
Q1) Which of the following is NOT true of a perfectly
competitive firm?
A)
B)
C)
D)
E)
It faces a perfectly elastic demand curve.
It is unable to influence the market price of the good it sells.
It seeks to maximize revenue.
Relative to the size of the market, the firm is small.
The firm’s only decision is how much output to produce.
Ans: C
• (A) is correct. Each firm in a perfectly competitive market is
facing a horizontal demand for its products.
• The demand is perfectly elastic because firms are selling
homogeneous goods. It is very easy for the customers to find
substitutes.
• Note that the MARKET DEMAND is not horizontal. Only the
demand for individual firms’ products is perfectly elastic.
• (B) and (D) are the features of a perfectly competitive market.
• In a perfectly competitive market, there is a huge number of
firms and each firm is of a minuscule size (compared to the
whole market)
• Because each firm is so small, none of its action can influence
the market. The firm will suffer if it deviates from the market
price. There will not be any effect on the market price if the
firm varies its output level.
• Therefore, (B) and (D) are true.
• (E) is also true. Indeed, when each firm is facing a given
market price, what it can do is to determine how much output
it is going to supply.
• The decision on output is made based on the firm’s cost
function.
• A rational economic agent will always aim at maximising
profits.
• Is maximizing profit the same as minimizing cost?
• What is the output level at which cost of production is
minimized?
• Zero output !!
• Thus maximizing profit is not the same as minimizing cost!!
• As mentioned just now, firms always aim at maximising
PROFITS.
• However, it does not mean that they aim at maximising
REVENUE. (Profit is the difference between revenue and
costs)
• i.e. Firms can maximize TR by increasing the production, but
the expenses incurred in order to earn more may be more
than the actual earnings.
• Therefore, (C) is the only option that is NOT true.
Additional Question #2
Q2)The Law of Diminishing Marginal Returns…
A)
B)
C)
D)
E)
Is a Long Run concept.
Applies only to small and medium sized firms.
Is a Short and Long Run concept.
Applies only to large firms.
Is a short run concept.
Ans: E
• The Law of Diminishing Marginal Returns states that…
• In a production where there are fixed and variable factors,
when more variable factors are added, additional output
yielded by each marginal unit of input drops eventually.
• Does the Law of Diminishing Marginal Returns have anything to
do with firm size?
• NO!
• LDMR holds whenever a firm has both fixed and variable
factors of production, regardless of size.
• Firms of any size can be using (or not using) both fixed and
variable factor input.
• Hence, (B) and (D) can be eliminated because they are wrong.
• (A), (C) and (E) are all about Long / Short Run.
• What is Short Run? What is Long Run?
Short Run
Long Run
Fixed Factor
Yes
?
?No
Variable Factor
?
Yes
?Yes
• Recall that LDMR describes a situation at which both fixed and
variable factors are in used.
• So is it referring to Long Run or Short Run?
• Short Run
• Therefore, the answer is (E).
Additional Question #3
Q3) Suppose a firm is collecting $1999 in Total Revenue and the
Total Cost of its fixed factors of production falls from $500
to $400. One can speculate that the firm will…
A)
B)
C)
D)
E)
Expand output.
Lower Price.
Earn greater profits or smaller losses.
Contract output.
Earn smaller profits or great losses.
Ans: C
• First of all, how are production decisions made by firms in
economics?
• Firms make production decisions based on a universal rule:
MC=MR
• For a price taker, its marginal revenue is always equal to the
price (MR=P)
• Therefore, the firm only has to determine its output level.
The optimal level of output is where MC = MR.
• Now that the fixed cost of production has decreased.
• Is the Marginal Cost (MC) schedule affected by any means?
• NO!
• So would the previous Q determined by MC=MR be affected?
• NO!
• Therefore, (A) and (D) can be eliminated as they are the
wrong answers.
• Output level is not affected by a change in fixed costs.
• This is because a change in fixed costs has no effect on
marginal cost of output.
• How about option (B)?
• Since we are talking about Perfect Competition (Price Taker)…
• Does the firm have any say on its price?
• No!
• Therefore, (B) is also not the answer.
• That leaves us with options (C) and (D).
• Recall that Profit = Revenue – Costs
• Now that (Fixed) Costs have dropped…
• What happens to Profit?
• Increases!
• Hence (C) is the correct answer.
Chapter 6 Problem 2
A price-taking firm makes air conditioners. The market price
of one of their new air conditioners is $120. Its total cost
information is given in the table below:
Air conditioners per day
Total cost ($ per day)
1
100
2
150
3
220
4
310
5
405
6
510
7
650
8
800
How many air conditioners should the firm produce per day
if its goal is to maximize its profit?
To decide how many air conditioners should produce in order to
maximize its profit, we can
1) Apply the cost-benefit principle ,or,
2) Calculate the profit levels and choose the production level that
gives the largest profit
Method 1:
The cost – benefit principle, we know that firm should continue to
produce an additional unit of goods as long as the additional
benefit to produce the good is at least as great as the additional
cost to produce the same good.
That is, MB > MC
At the market price of $120 for one air conditioner, perfectly
competitive firm can sell as many air conditioners as they wish in
order to maximize its profit.
The MB from selling an additional air conditioner is $120.
• To calculate the MC:
Air conditioners/day
Total Cost ($/day)
MC ($/day)
1
100
100
2
150
50
3
220
70
4
310
90
5
405
95
6
510
105
7
650
140
8
800
150
• By comparing the MB ($120) and the MC, the optimal output for this
firm to produce is 6 air conditioners per day.
• The MC of each of the first 6 air conditioners produced each day is
$105, which is less than the MB of $120. MB ($120) > MC ($105)
• Method 2) Calculate the profit:
• Profit = TR – TC
Air
conditioners/day
Total Cost
($/day)
Total Revenue
($/day)
Profit
($/day)
1
100
120
20
2
150
240
90
3
220
360
140
4
310
480
170
5
405
600
195
6
510
720
210
7
650
840
190
8
800
960
160
• In order to maximize its profit, this firm should produce 6 air
conditioners per day, since it yields the largest profit among the
others, $210/day.
• Same result as by applying the cost-benefit principle.
Chapter 6, Problem 3
• The Paducah Slugger Company makes baseball bats out of
lumber supplied to it by Acme Sporting Goods, which pays
Paducah $10 for each finished bat. Paducah’s only factors of
production are lathe operators and a small building with a
lathe. The number of bats per day it produces depends on the
number of employee-hours per day, as shown in the table
below.
# of bats per day
# of employee-hours per day
0
0
5
1
10
2
15
4
20
7
25
11
30
16
35
22
a) If the wage is $15 per hour and Paducah’s daily fixed cost for
the lathe and building is $60, what is the profit-maximizing
quantity of bats?
Quantity
(bats/day)
Total
Revenue
($/day)
Total labor cost
(hours X wage)
Total cost
(labor cost +
fixed cost)
Profit ($/day)
(revenue –
cost)
0
0
0 *15 = $0
0 + 60 =$60
-$60
5
50
1 *15 = $15
15 + 60 =$75
-$25
10
100
2 *15 = $30
30 + 60 =$90
$10
15
150
4 *15 = $60
60 + 60 =$120
$30
20
200
7 * 15 = $105
105 + 60 =$165
$35
25
250
11 *15 = $165
165 + 60 =$225
$25
30
300
16 *15 = $240
240 + 60 =$300
$0
35
350
22 *15 = $330
330 + 60 =$390
-$40
b) If the firm’s fixed cost decreases from $60 to $30, what is the
profit maximizing quantity of bats?
• Decrease in fixed cost will increase the profits across different
quantities of bats by the same amount ($30)
Quantity
(bats/day)
Total
Revenue
($/day)
Total labor
cost (hours X
wage)
Total cost
(labor cost +
fixed cost)
Profit ($/day)
(revenue –
cost)
0
0
0 *15 = $0
0 + 30 =$30
-$30
5
50
1 *15 = $15
15 + 30 =$45
$5
10
100
2 *15 = $30
30 + 30 =$60
$40
15
150
4 *15 = $60
60 + 30 =$90
$60
20
200
7 * 15 = $105
105 + 30 =$135
$65
25
250
11 *15 = $165
165 + 30 =$195
$55
30
300
16 *15 = $240
240 + 30 =$270
$30
35
350
22 *15 = $330
330 + 30 =$360
-$10
Chapter 6 Problem 4
In the preceding problem (3), how would Paducah’s profitmaximizing level of output be affected if the government imposed a
tax of $10 per day on the company? (Hint: Think of this tax as
equivalent to a $10 increase in fixed cost.) What would Paducah’s
profit-maximizing level of output be if the government imposed a
tax of $2 per bat? (Hint: Think of this tax as a $2-per-bat increase
in the firm’s marginal cost.) Why do these two taxes have such
different effects?
Fixed cost:
• Cost on all fixed Factor of Production, ex., lease payment on
machines, buildings
• Not depends on firm’s output
• A sunk cost
Variable cost:
• Cost on all variable Factor of Production, e.g., labor cost, input cost
• Depends on firm’s output
• Varied with number of products that firm produces
• Government imposed a tax of $10 per day (increase in fixed
cost)
• Will this tax affected the optimal level of output?
• Will this tax affected the cost of production?
• A tax of $10 per day would decrease its profit by $10 per day at
every level of output.
• The profit-maximizing level of output would still be 20 bats per day
(from Q3)
• This tax does not depends on the output, like a fixed cost or a sunk
cost.
• If Fixed cost changes, MB and MC will not be affected
• That is, this tax does not change the marginal cost, and hence, does
not change the profit-maximizing level of output if the firm
continues to produce.
Government imposed a tax of $10 per day
Quantity
(bats/day)
Total
Revenue
($/day)
Total labor cost
(hours X wage)
Total cost (labor
cost + fixed cost)
Profit ($/day)
(revenue –
cost)
0
0
0 *15 = $0
0 + 60 +10 =$70
-$70
5
50
1 *15 = $15
15 + 60 +10 =$85
-$35
10
100
2 *15 = $30
30 + 60 +10
=$100
$0
15
150
4 *15 = $60
60 + 60 +10=$130
$20
20
200
7 * 15 = $105
105 + 60 +10
=$175
$25
25
250
11 *15 = $165
165 + 60 +10
=$235
$15
30
300
16 *15 = $240
240 + 60 +10
=$310
$-10
35
350
22 *15 = $330
330 + 60 +10
=$400
-$50
• Tax of $10 decreases its profit by $10 per day at every level of output.
• It’s profit-maximizing output level is still at 20 bats per day.
•Fixed cost is independent of output
• Government imposed a tax of $2 per bat (increase in
marginal cost)
• Will this tax affected the optimal level of output?
• Will this tax affected the cost of production?
• A tax of $2 per bat would increase its cost of production.
• On every bat produces, additional $2/bat has to be added towards
the production cost.
• The marginal cost increases.
• The profit-maximizing level of output would decrease
• This tax depends on the output
Government imposed a tax of $2 per bat
Quantity
(bats/day)
Total
Revenue
($/day)
Total labor cost
(hours X wage) + $2
per bat
Total cost (labor
cost + fixed cost)
Profit ($/day)
(revenue – cost)
0
0
0 *15 + 2*0= $0
0 + 60 =$60
-$60
5
50
1 *15 + 2*5= $25
25 + 60 =$85
-$35
10
100
2 *15 +2*10= $50
50 + 60 =$110
-$10
15
150
4 *15 + 2*15= $90
90 + 60 =$150
$0
20
200
7 * 15 +2*20= $145
145 + 60 =$205
-$5
25
250
11 *15 +2*25= $215
215 + 60 =$275
-$25
30
300
16 *15 +2^30= $300
300 + 60 =$360
-$60
35
350
22 *15 +2*35= $400
400 + 60 =$460
-$110
• Tax of $2 per bat, the profit-maximizing output level falls to 15 bats
per day, with profit = $0.
•Variable cost depends on output.
• With Tax of $10 per day (increase in fixed cost)
• Profit-maximizing level of output stays the same
• With Tax of $2 per bat (increase firm’s MC)
• Profit-maximizing level of output falls
• The different effects are due to the nature of the Factor of
Production.
What if…
• government imposed a tax of $20 per bat (think of this tax as
equivalent to increase in marginal cost.)
Bats
(per day)
Total Revenue
($/day)
Total Variable cost
($/day)
Fixed Cost
($/day)
Total Cost
($/Day)
Profit
($/day)
0
0
0 +20(0)=0
60
60
-60
5
50
15 +20(5)=115
60
175
-125
10
100
30 +20(10)=230
60
290
-190
15
150
60 +20(15)=360
60
420
-270
20
200
105 +20(20)=505
60
565
-365
25
250
165 + 20(25) = 665
60
725
-475
30
300
240 + 20(30) = 840
60
900
-600
35
350
330 + 20(35) = 1030
60
1090
-740
TR < VC for all level of Q.
If this firm continues to operate, it would suffer an even greater loss.
This firms should shutdown and loss equals to the fixed cost, $60.
Chapter 6 Problem 6
Calculate daily producer surplus for the market for pizza
whose demand and supply curves are shown in the graph.
Price ($/slice)
S
6
3
D
0
12
24
Quantity (1,000s of
slices/day)
• Producer Surplus:
• The economic surplus received by sellers.
• If the price exceeds MC, the firm receives a producer surplus.
• It is the difference between price that sellers receive (market price)
and the lowest price that the sellers are willing to sell (reservation
price or marginal cost).
• To calculate producer surplus:
• The area below the market price and above the supply curve.
Price ($/slice)
S
6
3
D
0
12
24
Quantity 1000s slice
per day
Producer surplus:
The area of the shaded triangle:
($3/slice) (12,000 slices/day) (1/2) = $18,000 slices /day
Chapter 6 Problem 8
For the pizza seller whose marginal, average variable, and
average total cost curves are shown in the accompanying
diagram, what is the profit-maximizing level of output and
how much profit will this producer earn if the price of pizza is
$0.80 per slice?
MC
Price ($/slice)
ATC
AVC
1.03
0.80
0
360
Quantity (slices/day)
•
•
•
•
Assume it is a perfectly competitive market
Firms are price taker
It is a profit-maximizing firm
Goal is to maximize the amount of profit it earns
• The optimal level of output that maximizes profit, when,
P = MC
• Firms earn profit when,
P > ATC where Q is at optimal level of output
• Firm’s Short-run shutdown condition:
P < Min. AVC
•
•
•
•
This firm is suffering a lost:
P < ATC
Will this firm shutdown in the short-run?
NO. P > min. AVC
What is the profit-maximizing output?
• Profit-maximizing output, is the point where P = MC.
• This firm will sell 360 slices per day to maximize it’s profit.
• How much profit will this firm earns if price of pizza is $0.80 per
slice?
• Profit = TR – TC
• TR = P x Q, TC = ATC x Q
• Profit = P x Q – ATC x Q
• Profit = ( P – ATC )Q
= ($0.80 - $1.03)(360 slices)
= - $82.8/day (loss)
MC
Price ($/slice)
ATC
AVC
1.03
Loss
0.80
0
360
Quantity (slices/day)
Chapter 6, Problem 9
For the pizza seller whole marginal, average variable, and
average total cost curves are shown in the accompanying
diagram, what is the profit-maximizing level of output and
how much profit will this producer earn if the price of pizza is
$0.50 per slice?
Price ($/slice)
MC
ATC
AVC
1.18
0.68
0.50
0
260
Quantity (slices/day)
• The firm shutdown point is at P = $0.68 per slice (where P =
AVC)
• The firm should shutdown at any point below $0.68
• If a slice of pizza is sold for only $0.50, the firm will definitely
not produce any pizza and shut down
• Because price is less than the minimum value of AVC, this
producer will shut down in the short run.
• If the firm shuts down, there will be no (average) variable cost
• By shutting down the plant, the firm will have a negative
profit that is exactly equal to the fixed cost
• Fixed cost = Total cost – variable cost
• Total cost
– ATC * Q
– $1.18 / slice * 260 slices = $306.80 / day
• Variable cost
– AVC * Q
– $0.68 / slice * 260 slices = $176.80 / day
• Fixed cost = $306.80/day - $176.80/day =$130/day
• Thus, by shutting down the plant in the short run, the firm will
loss $130 a day
• In other words, the firm earns a profit of -$130 per day if the
price for a slice of pizza is just $0.50
Chapter 6 Problem 10
For the pizza seller whose marginal, average variable, and average
total cost curves are shown in the accompanying diagram (who is
the same seller as in problem 9), what is the profit-maximizing level
of output and how much profit will this producer earn if the price of
pizza is $1.18 per slice?
MC
ATC
Price ($/slice)
AVC
1.18
0.77
0.68
0.50
0
260
435
Quantity (slices/day)
This firm will sell 435 slices per day to maximize it’s profit.
• This firm is making profit:
• P > ATC
• The profit-maximizing output is 435 slices if price of
pizza is $1.18 per slice
•
•
•
•
•
Total profit:
Profit = TR – TC
TR = P x Q
TC = ATC x Q
Profit = (P - ATC) x Q
MC
ATC
Price ($/slice)
AVC
1.18
?
0.77
0.68
0.50
0
260
435
Quantity (slices/day)
This firm will sell 435 slices per day to maximize it’s profit.
• ATC at the profit-maximizing level of output:
• Recall, TC = FC + VC
• At the optimal level of output, 435 slices, AVC equals to
$0.77 per slice
• VC = AVC x Q
VC = $0.77 x 435 slices
VC = $334.95
• Recall from Q9, the firm’s FC = $130 per day
• Total cost:
• $130 + $334.95 = $464.95
• Total profit at price of $1.18 per slice and output 435 slices:
• Profit = TR – TC
• TR = P x Q
= $1.18 x 435 slices
= $513.3
• Profit = $513.3/day - $464.95/day = $48.35
Additional Question #4
According to the graph below, if market price of sweater is $20.
What is the profit-maximizing output? How much profit will this firm
make? What should be the shutdown point for this firm?
MC
ATC
Price ($/sweater)
AVC
$20
17
15
0
5
6
8
Quantity (sweater/day)
• At price $20, the profit-maximizing output is 8 sweaters
per day
• At price $20, P = MC = ATC
• This is the firm’s breakeven point, total revenue equals
total cost
• It earns zero economic profit
•
Economic profit = Total Revenue – Explicit Costs – Implicit Costs
(More on Chapter 8…)
•
Shutdown point: the output and price at which the firm just
covers its total variable cost. Firm is indifferent between
continuing operations and shutting down.
P = MC = min. AVC
•
•
•
At price $17, P = min. AVC,
Both price and AVC equal $17, the firm just covers its TVC
The firm is indifferent on staying or shutting down
•
At the shutdown point, firm usually incurs loss. How could it be
able to cover its TVC?
As long as the Unit Contribution Margin equals to zero, this is the
firm’s shutdown point.
•
•
•
Unit Contribution Margin = Unit Revenue (Unit Price) – Unit
Variable Cost (AVC)
•
Any point below the shutdown point, the firm should
shutdown.
•
•
•
At price $15, P < min. AVC,
Firms cannot even cover its TVC
It should shutdown and the loss equals to fixed cost
•
•
Therefore, the shutdown point is at $17
Any price below $17, the firm should shutdown
MC
ATC
Price ($/sweater)
AVC
Breakeven Point
$20
Shutdown Point
17
15
0
5
6
8
Quantity (sweater/day)
End of Chapter 6