Theory of the Firm• Theory of the firm attempts to explain how firms react to

levels of prices and changes to prices

• This is eventually used to explain why supply curves look like they do

• Used to develop our understanding of economic theory further

Theory of the Firm

• Firms– Think of as legal entities

• Types1) Proprietorships2) Partnerships 3) Corporations– Proprietorships & partnerships are easy to set up, but do not have

unlimited liability– Corporations have unlimited liability– For this course, assume all firms are Corporations

• What do firms Do? – Maximize Profits

Theory of the Firm

• Profit Function:Max (Revenues – Costs)

• Production FunctionQ = F(L, K)– Output (Q) is a function of Labour (L) and Capital (K)

• Recall that in the short-run, capital is fixed but labour is variable Q = F(L, K)

Means fixed

Breaking Down the Profit Function

• Profit Function:Max (Revenues – Costs)

• Revenues:– Revenue = P x Q– Higher prices and higher sales lead to bigger Revenues

• Costs:– Costs are related to output (Q)– The more output the more labour (L) & capital (K) (Costs) incurred

Short-run Analysis of Production Function

0

• Capital is fixed in the short-run• To increase output, need to

increase labour• Overtime, hire short term

workers, etc. • Increases output of factories,

etc. (Capital)• Note that there are decreasing

returns as you add more labour (i.e., machines maxed out, people running into each other, etc.)

L

QQ = F(L,K)

Decreasing additional

output from more labour

Resulting Cost Function

0

• With capital fixed in short-run, diminishing returns to added labour

• Increased labour means increased costs

• Hence, quadratic like function

Q

CostC = ~F(L)

Increasing cost with

increasing labour

Average Product of Labour

0

• To find average product of labour APL, draw a ray from the origin to where the company is operating at

• TP = Total Production

L

Q TP

Q/L = APL

Decreasing ATC

Q2

Q1

Q3

L1 L2 L3

Average Product of Labour

0

• Where the ray from the origin measures the APL, the marginal product of labour (MPL) is measured by the slope of the tangent to the curve at that point

L

Q TP

MPL = ΔQ/ ΔLQ2

Q1

Q3

L1 L2 L3

Maximum Average Product of Labour

0

• The maximum APL occurs where the ray is tangent to the curve (short run)

• This is the point where the output per person for that amount of labour is max

• (i.e., best average output without running into each other, etc.)

L

Q Q = F(L,K)

Max APL

Q2

Q1

Q3

L1 L2 L3

Maximum Marginal Product of Labour

0

• The maximum MPL occurs where the slope of the curve is greatest (i.e, at the inflection point)

• This is the point where the amount of output from the next additional unit of labour, is the greatest

L

Q TP

Q2

Q1

Q3

L1 L2 L3

Max MPL

MPL and APL

0

• The APL and MPL curve appear as such

• The maximum MPL occurs at L*, whereas the max APL occurs at Lo

• Relationship (for increasing L): • When marginal value > ave value,

then average is increasing• When marginal value < ave value,

then average is decreasing • When marginal value = ave value,

then the APL is at its maximum

L

Q TP

L0

PL

MPL Curve

APL Curve

L* Lo

ΔQ/ ΔL (Max)

Q/L (Max)

Short-run Analysis of Production Function

0

• ATC function corresponds to production function with increasing labour

• (i.e., raising output in the short-run by adding additional labour)

• TP = Total Production

L

Q TP

Increasing ATC

Decreasing ATC

Average Cost Function

0

• The relationship between MPL and APL have the following implications for cost

• Average Cost (AC)• At A, output (Q) rising

faster, relatively to the rise in total cost TC

• At B, output (Q) rising slower relative to rise in TC

• Corresponds to production function (see next slide)

Q

Average Cost

AC

Increasing cost with increasing output

(by increasing labour)

A B

Average Fixed Costs

0

• Up until now we have assumed labour has been the only cost but in reality most production processes have fixed costs

• Fixed costs are incurred even if no production (e.g., building rent, utilities)

• the average fixed cost declines as production quantities increase (spread over more units)

• Analysis of fixed costs is often important in answering the question of “what scale should we be operating in?”

Q

Average Fixed Cost

AFC = FC/Q

Average Total Cost

Q

Q

Q

AFC AVC

ATC

+

=ATC = AVC + AFC

AFC = FC/QAVC = VC/Q

• Cost analysis is a big focal point of microeconomics and management

• The reason being is that cost data is readily available to operating businesses

Average Variable Cost

0 Q

Average CostSo, AVC = TVC/Q ~

$ x L/Q

Where $ is wage

APL

Also APL = Q/L

Hence, AVC is about equal to ~

$ x 1/APL

Called “scaled inverse function”

Q

APL

AVC

Marginal Cost Curve

0

• Marginal Cost = Additional Cost of producing one more unit

• Similar to MPL & APL, (for increasing Q) when MC < ATC, then ATC is falling, and when MC is greater than ATC, ATC is rising.

Q

$ MC

0 Q

$ MC

ATC

Production Cost Analysis

0 Q

$ MC

AVC

ATC

FC

Marginal Cost Curve

• For price taking firms (get $P1 for any unit sold), an analysis of production capacity at the margin can indicate what level to produce at

• Say production initially at Q1, and raise to Q2

• Extra revenue = (Q2-Q1)*P1 • Additional profit (see graph)• Additional cost (see graph)• So additional revenue is > than

additional cost, therefore raise production to Q2

0Q

$MC

P1

Q1 Q3Q2

Additional Profit

Additional Cost

Marginal Cost Curve

• Say production now at Q2 and decide to raise to Q3

• Extra revenue = (Q3-Q2)*P1 • Additional cost (see graph)• So additional revenue is < than

additional cost, therefore don’t raise production to Q3

• So given a price P1, should produce Q2

0Q

$MC

P1

Q1 Q3Q2

Additional Cost

Marginal Cost Curve• If price were to rise to P3,

then optimal to produce at Q3• If price were to fall to P2, then

optimal to lower production to Q1

• MC curve provides a relationship between P&Q

• To maximize profit, a price taking firm should set production to the quantity where MC=P

• What kinds of firms are price takers? E.g. agriculture, commodities – Perfect Competition

0Q

$MC

P1

Q1 Q3Q2

P2

P3

Marginal Cost Curve

• For a price P1 with production at Q1, the revenue to the firm will be Q1xP1

• The profit for the firm will be the rectangle above the point on the ATC curve (as shown)

• The cost to the firm will be the rectangle below the point on the ATC curve

0Q

$MC

P1

Q1

Q3

AVC

ATC

Marginal Cost Curve• Is the MC Curve = to the

firms supply curve?• Yes, if it is the portion above

the AVC• If a firms has a AVC > P, then

it will not be able to meet payroll and will effectively go into bankruptcy

• This is not necessarily true for when P is in between AVC & ATC, as a firm will continue to operate in the short term in order to minimize losses

0Q

$MC

P1

Q1

Q3

AVC

ATC

Average Total Cost

QQ

P$

+

MARKET SC

• What will be the market supply curve? • Horizontal summation of individual firm supply curves• For profitable industries, firms will enter the market and the supply

curve will shift out (to the right)• For unprofitable industries, firms will exit the market and the supply

curve will shift in

P$ P$ P$

Q Q8 12 9 13 5 10 22 35

+ =

Individual Firm Supply Curves

Comparative Statics

• Suppose there was a change in the costs for an industry (e.g., lower energy costs)

• The MC and ATC for a firm would shift as shown

• The market supply curve will shift as well, resulting in a lower market price and a higher quantity

• Dynamics: costs decline, 1 firm lowers price, all other firms must then match price

0 Q

$MC

ATC’ATC

MC’

Q

P$S2

S1

D

Q2Q1

P2

P1

Comparative Statics

• In general , 3 common types of industry changes that will affect the market supply curve

• 1) Change in number of firms• 2) Change in costs• 3) Change in technology

(usually considered like a change in costs)

• All affect supply curve and change market similar to as discussed before.

0Q

P$S1

D

S2

S3

Q2Q3 Q1

P3

P1

P2

Market vs Individual Demand Curve

Q

MARKET DC

• For a Price Taking firm, their demand curve is a flat line at the market price

• The market demand curve however, is downward sloping • For the price taking firm, they observe price (i.e., no pricing power)• Pm = market Price

P$ P$

Q

Individual Firm Demand Curve

D

S

Firm DCPm

S

Marginal Cost Curve• Assume free entry and exit into a

market• ATC includes production costs,

managerial costs and entrepreneurial opportunity costs (i.e., includes a reasonable return on investment)

• Hence, market entry & exit will be balanced when ATC = Pm and therefore “Economic Profit” = 0

• For a firm in a perfectly competitive market (TC=Q1*ATC) and (TR=Q1*P1);

• Economic Profit = TR – TC = 0

0Q

$MC

Pm

Q1

Q3

ATC

Market Entry

MARKET

• Does this make sense? Yes because Economic Profit or “Super Profit” is profit over and above entrepreneurial costs

• If there is “Economic Profit” in a perfectly competitive industry we would expect more firms to enter

• 1) Assume “Economic Profit” present

P$

Qm

Individual Firm

D

S

0Q

Pm

Q1

MC

ATCPm

P$Economic Profit

Market Entry / Exit

MARKET

• Since there is “Economic Profit” in the industry, there is incentive for entrepreneurs to start new firms and enter the market

• Market Supply curve shifts out (S to S’) & Pm lowers to Pm’ • Firms will enter the market until no more Economic Profit present• At equilibrium there is only “Accounting Profit” and TR = TC

P$

Qm

Individual Firm

D

S

0Q

Pm

Q’

MC

ATCPm

P$ Economic Profit now 0 as TR = TC

S’

Pm’ Pm’

Market Exit

MARKET

• Assume that sustained high energy costs have raised the cost structure for some firms in a specific market

• now for these firms (ATC > Pm) & TC > TR = Economic Loss• These firms will exit the market

P$

Qm

Individual Firm

D

S

0Q

Pm

Q1

MC

ATCPm

P$Economic Loss

Market Exit

MARKET

• These firms exit the market and therefore the market supply curve shifts in to S’ and market price raises to Pm’

• This restores equilibrium to the market

P$

Qm

Individual Firm

D

S

0Q

Pm

Q

MC

ATCPm

P$S’

Pm’ Pm’

Qm’

Summary• For Perfect Competition assume

free entry or exit• P = ATC = MC• Perfect Competition:

Homogeneous market, Large number of buyers & sellers, free entry & exit

• Commoditization: products that once weren’t homogenous, but as competition evolves, these products become standardized

• (e.g., computer storage)0

Q

$MC

Pm

Q1

Q3

ATC