perfectly competitive supply: the cost side of the market

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Perfectly Competitive Supply: The Cost Side of The

Market

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Profit-Maximizing Firms and Perfectly Competitive Markets

A profit-maximizing firm is one whose primary goal is to maximize profit, i.e. total revenue minus total cost.

A perfectly competitive market is one in which no individual supplier has any influence on the market price of the good.

Characteristics of Perfectly Competitive Market

Homogeneous productMany buyers and sellers, each of which

buys or sells only a small fraction of the total quantity exchanged

Buyer and sellers are well-informed Rapid dissemination of accurate information

at low cost

Free entry and exit into the marketProductive resources are mobile

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Profit-Maximizing Firms and Perfectly Competitive Markets

A price taker is a firm that has no influence over the price of the product that it sells.

Laundry Art reproduction

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Factors of production

Factors of production are inputs used in the production of a good or service.

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Fixed factor of production

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

E.g., buildings or plants

Example: Transmission tower for a student radio station.

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Variable factor of production

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

E.g., workers or raw materials or plants

Example: Music library for a student radio station.

Total Product and Marginal Product

Total Product (TP)The quantity of output produced by the firm in

a given period of time.The total output is related to the input level of

the fixed and variable factors of production

Marginal Product (MP)The increase in total product due to hiring of one

additional unit of the variable factor (assuming quantities of other factors are constant)

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The Law of Diminishing Returns

Total no. of employees/d

ay

Total no. of

bats/Day(TP)

Additional no. of

bats/day(MP)

0 0

1 40 40

2 100 60

3 130 30

4 150 20

5 165 15

6 175 10

7 181 6

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 the quantities of all other factors are fixed.

Short Run and Long Run

Short Run (SR)A period of time over which at least one factor is fixed.

Long Run (LR)A period of time over which all factors are variable.

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Example: 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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Fixed Cost

Suppose the lease payment for the Louisville Slugger’s lathe and factory is $80 per day.

This payment is a fixed cost (since it does not depend on the number of bats per day the firm makes)

FC = rK

r: Price of renting a unit of capital service (rental rate)K: No. of unit of the capital service

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Variable Cost

The company’s payment to its employees is called variable cost, because unlike the fixed cost, it varies with the number of bats the company produces.

VC = wL

w: Price of hiring a unit of labor service (wage rate)

L: No. of unit of labor service

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Total Cost

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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Marginal Cost

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: Louisville Slugger

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: Louisville Slugger

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 (=24/40)

2 100 80 48 128 0.4(=24/60)

3 130 80 72 152 0.8(=24/30)

4 150 80 96 176 1.2(=24/20)

5 165 80 120 200 1.6(=24/15)

6 175 80 144 224 2.4(=24/10)

7 181 80 168 248 4.0(=24/6)

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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: Louisville Slugger (Continued)

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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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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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

According to the law of diminishing returns, marginal cost increases as the firm expands production.

The firm's best option is to keep expanding output as long as marginal cost is less than price, i.e. marginal benefit of production.

In equilibrium, the profit maximizing output level for a perfectly competitive firm:

P = MC

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Caveat: Production at a loss when P=MC

If the company's fixed cost was more than $213.50 per day (say, $300/day), 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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Choosing Output to Maximize Profit in the SR

In the short run (SR), the fixed cost is unavoidable and does not affect the output decision in the SR.

As the firm’s fixed cost is a sunk cost, the firm’s 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 continues to face the same situation in the long run (LR), it would be better for the firm to get out of the bat business completely as soon as its equipment lease is expired.

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Shut-Down Condition in the Short Run

It might seem that a firm that can sell as many 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 is an exception to this rule.

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Shut-Down Condition in the Short Run

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 shut down its production By shutting down, it will suffer a loss equal to its fixed cost. By continuing production, it would suffer an even larger

loss (than its fixed cost).

Shutdown Condition:Shut down production if total revenue is less

than variable costs.

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Choosing Output to Maximize Profit in the LR

Average total cost:

ATC = TC/Q.

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

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

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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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Modified Louisville Slugger Example

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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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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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 any 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

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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

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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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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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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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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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End

perfectly competitive supply: the cost side of the market

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