1 Introductory Microeconomics Perfectly Competitive Supply: The Cost Side of The Market.

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Introductory Microeconomics

Perfectly Competitive Supply: The Cost Side of The

Market

2

Example 6.1. How should Leroy divide his time between…

…picking apples… …and writing pulp fiction?

Note: Pulp magazines (or pulp fiction; often referred to as “the pulps”) were inexpensive fiction magazines. They were widely published from the 1920s through the 1950s. The term pulp fiction can also refer to mass market paperbacks since the 1950s. (from Wikipedia)

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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 apples he harvests.

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.

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Earnings aside, Leroy is indifferent between the two tasks.

The amount of apples he can harvest depends on the number of hours he devotes to this activity:

Hours Total bushels Additional bushels

1 8 8

2 12 4

3 15 3

4 17 2

5 18 1

5


For example, if apples sell for $2.50 per bushel:

Hours Total bushels

Additional bushels

1 8 8

2 12 4

3 15 3

4 17 2

5 18 1

$ for the additional hour

20 = 8x2.5

10 = 4x2.5

7.5 = 3x2.5

5 = 2x2.5

2.5 = 1x2.5 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.

Leroy will devote only the first hour to picking apples. That is, a total of 8 apples.

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If the price of apples then rose to $5 per bushel:

Hours Total bushels

Additional bushels

1 8 8

2 12 4

3 15 3

4 17 2

5 18 1


40 = 8x5

20 = 4x5

15 = 3x5

10 = 2x5

5 = 1x5 It would pay Leroy to devote a second hour to picking,

which would mean a total of 12 bushels of apples.

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Once the price of apples reached $6.67 per bushel

Hours Total bushels

Additional bushels

1 8 8

2 12 4

3 15 3

4 17 2

5 18 1


53.36 = 8x6.67

26.68 = 4x6.67

20.00 = 3x6.67

13.34 = 2x6.67

6.67 = 1x6.67 Leroy would devote a third hour to picking apples, for a

total of 15 bushels.

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If the price rose to $10 per bushel

Hours Total bushels

Additional bushels

1 8 8

2 12 4

3 15 3

4 17 2

5 18 1


80 = 8x10

40 = 4x10

30 = 3x10

20 = 2x10

10 = 1x10 Leroy would devote a fourth hour to picking apples, for a

total of 17 bushels.

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If the price rose to $20 per bushel

Hours Total bushels

Additional bushels

1 8 8

2 12 4

3 15 3

4 17 2

5 18 1


160 = 8x20

80 = 4x20

60 = 3x20

40 = 2x20

20 = 1x20 Leroy would devote a fifth hour to picking apples, for a total

of 18 bushels.

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Leroy's individual supply curve for apples relates the amount of apples he is willing to supply at various prices.

20.00

2.505.006.67

10.00

P ($/bu)

Q (bu/day)

Leroy's supply curve for apples

8 12 1517

18

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Marginal cost can be computed:

Hours

Total bushels

Additional bushels

1 8 8

2 12 4

3 15 3

4 17 2

5 18 1

Marginal cost (of an additional

bushel)

$2.5=$20/8

5=20/4

6.67=20/3

10=20/2

20=20/1

The perfectly competitive firm’s supply curve is its marginal cost curve.

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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.

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Example 6.2.

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?

20.00

2.505.006.67

10.00

P ($/bu)

Q (100s of bu/day)

Market supply curve for apples

8 12 1517

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Reasons for upward sloping supply

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.

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Supply and opportunity cost

At what price would Andy Lau consider it worth his while to pick apples?

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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.

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Profit-Maximizing Firms and Perfectly Competitive Markets

Definition. A price taker is a firm that has no influence over the price at which it sells its product.

Laundry Art reproduction

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Price setters

Intel microprocessorsMicrosoft operating systems

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Price setter vs. price taker

Apple iPod: Price setter

Generic USB MP3 player: price taker

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Factor of production

Definition. A factor of production is an input used in the production of a good or service.

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Fixed factor of production

Definition. A fixed factor of production is an input whose quantity cannot be altered in the short run.

Example: Transmission tower for a student radio station.

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Variable factor of production

Definition. A variable factor of production is an input whose quantity can be altered in the short run.

Example: Music library for a student radio station.

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Example 6.3. Louisville Slugger uses two inputs:

labor (e.g., woodworkers)…

and

capital (e.g., lathes, tools, buildings)

…into finished output (baseball bats). … to transform raw materials (e.g., lumber)

A lathe is a tool which spins a block of material to perform various operations such as cutting, sanding, knurling, or deformation with tools that are applied to the workpiece to create an object which has symmetry about an axis of rotation.

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The short-run production function

Total number of employees per

day

Total number of bats per

day

0 0

1 40

2 100

3 130

4 150

5 165

6 175

7 181

Note 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.

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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.

FC = rK

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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.

VC = wL

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The firm’s total cost is the sum of its fixed and variable costs:

Total cost = Fixed Cost + Variable Cost

TC = FC + VC

TC = rK + wL

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The firm’s marginal cost is the change in total cost divided by the corresponding change in output.

MC = TC/Q

MC = VC/Q

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Example 6.4.

If Louisville slugger pays a fixed cost of $80 per day, and to each employee a wage of $24/day, calculate the company’s output, variable cost, total cost and marginal cost for each level of employment.

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Example 6.4.

Employees per day

Bats per day

Fixed Cost ($ per day)

Variable Cost

($/day)

Total Cost ($/day)

Marginal Cost

($/bat)

0 0 80 0 80

1 40 80 24 104 0.6

2 100 80 48 128 0.4

3 130 80 72 152 0.8

4 150 80 96 176 1.2

5 165 80 120 200 1.6

6 175 80 144 224 2.4

7 181 80 168 248 4.0

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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.

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Example 6.5.

Suppose the wholesale price of each bat (net of lumber and other materials costs) is $2.50.

How many bats should Louisville Slugger produce?

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Example 6.5.

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).

Employees per day

Bats per day

Fixed Cost ($ per day)

Variable Cost

($/day)Total Cost

($/day)

Marginal Cost

($/bat)

0 0 80 0 80

1 40 80 24 104 0.6

2 100 80 48 128 0.4

3 130 80 72 152 0.8

4 150 80 96 176 1.2

5 165 80 120 200 1.6

6 175 80 144 224 2.4

7 181 80 168 248 4.0

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Example 6.5.

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

Output(bats/day)

Total revenue($/day)

Total cost

($/day)

Profit($/day)

0 0 0 80 -80

1 40 100 104 -4

2 100 250 128 122

3 130 325 152 173

4 150 375 176 199

5 165 412.50 200 212.50

6 175 437.50 224 213.50

7 181 452.50 248 204.50

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Choosing Output to Maximize Profit

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.

The profit maximizing output level for the perfectly competitive firm:

P = MC

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Note on Example 6.5.

Note in Example 6.5 that if the company's fixed cost had been any more than $293.50 per day (say, 300), it would have made a loss at every possible level of output.

Employees per day

Output(bats/day)

Total revenue($/day)

Total cost

($/day)

Profit($/day)

0 0 0 300 -300

1 40 100 324 -224

2 100 250 348 -98

3 130 325 372 -47

4 150 375 396 -21

5 165 412.50 420 -7.5

6 175 437.50 444 -6.5

7 181 452.50 468 -15.6

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Note on Example 6.5.

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.

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A Note on the Firm’s Shut-Down Condition

It might seem that a firm that can sell as much output as it wishes at a constant market price would always do best in the short run by producing and selling the output level for which price equals marginal cost.

But there are exceptions to this rule.

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Suppose, for example, that the market price of the firm’s product falls so low that its revenue from sales is smaller than its variable cost at all possible levels of output.

The firm should then cease production for the time being.By shutting down, it will suffer a loss equal to

its fixed costs. But by remaining open, it would suffer an even

larger loss.

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P = market price of the product

Q = number of units produced and sold

PxQ = total revenue from sales

Shutdown rule:Cease production if PxQ is less than VC for

every level of Q.

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Average Variable Cost and Average Total Cost

Suppose that the firm is unable to cover its variable cost at any level of output—that is, suppose that PxQ < VC for all levels of Q.

Then P < VC/Q for all levels of Q, since we obtain the second inequality by simply dividing both sides of the first one by Q.

The firm’s short-run shut-down condition may thus be restated a second way: Discontinue operations in the short run if the

product price is less than the minimum value of its average variable cost (AVC).

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Short-run shut-down condition (alternate version):

P < minimum value of AVC

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Profitability

Average total cost:

ATC = TC/Q.

Profit = total revenue – total cost = PxQ – ATCxQ= (P – ATC) Q

A firm can be profitable only if the price of its product price (P) exceeds its ATC.

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A Graphical Approach to Profit-Maximization

For Louisville Slugger, we have

Employees per

dayBats

per day

Variable Cost ($/day)

Avg Variable Cost ($/day)

Total Cost

($/day)

Avg Total Cost

($/bat)

Marginal Cost ($/bat)

0 0 0 0 80

1 40 24 0.6 104 2.6 0.6

2 100 48 0.48 128 1.28 0.4

3 130 72 0.554 152 1.169 0.8

4 150 96 0.64 176 1.173 1.2

5 165 120 0.727 200 1.21 1.6

6 175 144 0.823 224 1.28 2.4

7 181 168 0.927 248 1.37 4.0

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A Graphical Approach to Profit-Maximization

Properties of the cost curves:

The upward sloping portion of the marginal cost curve (MC) corresponds to the region of diminishing returns.

The marginal cost curve must intersect both the average variable cost curve (AVC) and the average total cost curve (ATC) at their respective minimum points.

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Price = Marginal Cost: The Maximum-Profit Condition

In earlier examples, we implicitly assumed that the firm could employ workers only in whole number amounts.

Under these conditions, we saw that the profit-maximizing output level was one for which marginal cost was somewhat less than price (because adding yet another employee would have pushed marginal cost higher than price).

But when output and employment can be varied continuously, the maximum-profit condition is that price be equal to marginal cost.

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Example 6.6.

For the bat-maker whose cost curves are shown in the next slide, find the profit-maximizing output level if bats sell for $0.80 each.

How much profit will this firm earn? What is the lowest price at which this firm would

continue to operate in the short run?

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Example 6.6.

AVCATC

$/bat

Bats/day

0.28

0.60

0.80

1.00

1.20

1.40MC

0.400.48

80 100 130

Price

150

1.32

The cost-benefit principle tells us that this firm should continue to expand as long as price is at least as great as marginal cost.

If the firm follows this rule it will produce 130 bats per day, the quantity at which price and marginal cost are equal.

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Example 6.6.

AVCATC

$/bat

Bats/day

0.28

0.60

0.80

1.00

1.20

1.40MC

0.400.48

80 100 130

Price

150

1.32

Suppose that the firm had sold some amount less than 130—say, only 100 bats per day.

Its benefit from expanding output by one bat would then be the bat's market price, 80 cents.

The cost of expanding output by one bat is equal (by definition) to the firm’s marginal cost, which at 100 bats per day is only 40 cents.

MB

MC

50

Example 6.6.

AVCATC

$/bat

Bats/day

0.28

0.60

0.80

1.00

1.20

1.40MC

0.400.48

80 100 130

Price

150

1.32

So by selling the 101st bat for 80 cents and producing it for an extra cost of only 40 cents, the firm will increase its profit by 80 – 40 = 40 cents per day.

In a similar way, we can show that for any quantity less than the level at which price equals marginal cost, the seller can boost profit by expanding production.

MB

MC

51

Example 6.6.

AVCATC

$/bat

Bats/day

0.28

0.60

0.80

1.00

1.20

1.40MC

0.400.48

80 100 130

Price

150

1.32

Conversely, suppose that the firm were currently selling more than 130 bats per day—say, 150—at a price of 80 cents each.

Marginal cost at an output of 150 is 1.32 per bat. If the firm then contracted its output by one bat per day, it would cut its costs by 1.32 cents while losing only 80 cents in revenue. As a result, its profit would grow by 52 cents per day.

MB

MC

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Example 6.6.

The same arguments can be made regarding any quantities that differ from 130.

Thus, if the firm were selling fewer than 130 bats per day, it could earn more profit by expanding; and that if it were selling more than 130, it could earn more by contracting.

So at a market price of 80 cents per bat, the seller maximizes its profit by selling 130 units per week, the quantity for which price and marginal cost are exactly the same.

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Example 6.6.

Total revenue = PxQ = ($0.80/bat)x(130 bats/day) = $104 per day.

Total cost = ATCxQ= $0.48/bat x 130 bats/day = $62.40/day

So the firm’s profit is $41.60/day.

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Example 6.6.

Profit is equal to (P – ATC)xQ, which is equal to the area of the shaded rectangle.

AVCATC

$/bat

Bats/day

0.80

MC

0.48

130

PriceProfit = $41.60/day

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Example: The Holiday Store at Tung Lung Island

Why does the store open only on holidays?

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SUPPLY AND PRODUCER SURPLUS

The economic surplus received by a buyer is called consumer surplus.

The analogous construct for a seller is producer surplus, the difference between the price a seller actually receives for the product and the lowest price for which she would have been willing to sell it (her reservation price, which in general will be her marginal cost).

Producer surplus sometimes refers to the surplus received by a single seller in a transaction, sometimes to the total surplus received by all sellers in a market or collection of markets.

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Example 6.7. Calculating Producer Surplus

How much do sellers benefit from their participation in the market for cashews?

Price($/lb)

Quantity(1000s oflbs/day)

0

D

S

2468

1012

2 4 6 8 12 16 20 24

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Example 6.7. Calculating Producer Surplus

For all cashews sold up to 8,000 pounds per day, sellers receive a surplus equal to the difference between the market price of $8 per pound and their reservation price as given by the supply curve.

Total producer surplus received by buyers in the cashew market is the area of the shaded triangle between the supply curve and the market pricePrice($/lb)

Quantity(1000s oflbs/day)

0

D

S

2468

1012

2 4 6 8 12 16 20 24

PS= (1/2)(8,000 lbs/day)x($8/lb) = $32,000/day

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Producer surplus

Producer surplus is the highest price sellers would pay, in the aggregate, for the right to continue participating in the cashew market.

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Supply is all about marginal cost.

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Does demand ever affect supply?

D

SP

Q

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Example 6.8.

Is the cost of a ticket to the NBA finals so high because the salaries of NBA players (such as YAO Ming) is so high?

63

Example 6.8.

Partly. But then why are the wages of NBA players so high?

Because so many people are willing to pay so much to be able to watch them.

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Example 6.8.

But a starving person would be willing to pay even more for food than for watching an NBA game.

Food is cheap and NBA games are expensive because many people can produce food, but only few have the skills to play in the NBA.

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Shaquille O’Neal: NBA star extraordinaire.

Earnings from basketball-related activities during last championship season: $25,000,000.

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Supply depends on costs and costs always depend on demand.

In many (perhaps most) cases the prices of the inputs required to produce a product will not be much affected by the demand for that product.

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The demand for bicycles will have no significant effect on the price of steel, an input for making bicycles, because the steel used in making bicycles is only a tiny fraction of the total amount of steel sold.

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So for most markets, we can assume that a shift in the demand curve will not lead to a shift in the supply curve.

Assume this independence, unless otherwise stated.

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End

1 Introductory Microeconomics Perfectly Competitive Supply: The Cost Side of The Market.

Documents

hour leroy

bushels of apples

additional hour

price of apples

harvesting apples

1x10 leroy

1x20 leroy

worth of apples