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Topic 1(b): Review of Producer Theory (supply)

Review of Supply.

• Three areas to cover on the supply side:

i. Interpreting an individual producer’s supply curve

ii. Measuring producer well-being using the supply curve

iii. Deriving aggregate supply from individual supply

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Topic 1(b): Review of Producer Theory i. Interpreting a firm’s supply curve

• Recall that a supply curve maps out a relationship between price and quantity.

Price (P)

Quantity (Q)

Supply curves usually slope upwards: known as the “law” of supply

i.e., firms that take the prices of output and inputs as given.

NB: Throughout this class we will only be looking at the supply behavior of competitive firms.

How to interpret this supply curve?

Like D curve, there are two interpretations of the S curve.

SupplyCurve (S)

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Topic 1(b): Review of Producer Theory

• The first interpretation of the supply curve is (again) probably most familiar:

P

Q

Interpretation 1: S curve tells us how many units of a good a producer wishes to sell in total, at a given price per unit for the good.

If the price per unit is P1, then the firm would like to sell Q1 units etc.

We can think of this interpretation as reading the S curve horizontally: that is, if we plug in values for P, we get out values for Q.

S

P1

Q1

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Topic 1(b): Review of Producer Theory

• The second interpretation of the supply curve should also be (relatively) familiar:

P

Q

Interpretation 2: the height of the S curve at any given point tells us how much additional units of the good cost to produce.

i.e., the supply curve is also a Marginal Cost (MC) curve.

If the firms is currently producing Q1 units of the good, then a small increase in quantity would cost P1 per unit to produce.

SP1

Q1

We can think of this interpretation as reading the S curve vertically: that is, if we plug in values for Q, we get out values for P.

Again, useful to work through an example.

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Topic 1(b): Review of Producer Theory

Example: Suppose that supply is given by Q = P - 5.

P($)

Q

From the S function, if P=$5, Q=0 will be supplied.

But if P = $6, Q = 1 will be supplied.

firm’s cost of supplying that first unit (the MC of that unit) is somewhere between $5 and $6.

S

And area under S curve from Q=1 to Q=2 equals cost of producing 2nd unit.

And area under S curve from Q=0 to Q=2 tells us how much the firm’s costs increase going from Q=0 to Q=2.

Turns out that the exact cost of producing this first unit = area under the S curve between Q=0 and Q=1.

1

5

6

7

2

$5.50 $6.50

$12

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Topic 1(b): Review of Producer Theory

• Area under S curve up to a given Q actually tells us the Variable Cost (VC) of producing that Q.

• Recall that a firm’s Total Costs (TC) have 2 components:TC = Fixed Costs + Variable Costs

= FC + VC.

• By definition, FC don’t change as Q changes, while VC do.

• So MC = TC/Q = (FC+VC) /Q = VC /Q.

area under the S curve up to a given Q = MC of 1st unit + MC of 2nd unit + MC of third unit etc. etc.

• And adding up MCs is the same as calculating VC.

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Topic 1(b): Review of Producer Theoryii. Measuring producer well-being using the supply curve.

P($)

Q

1st interpretation of S curve: tells us Q supplied at a given P.

If producer sells Q1 units at P1 per unit, then Total Revenue (TR) received = area of rectangle P1Q1.

2nd interpretation of S curve: area under S curve measures VC of producing Q1 units.

Definition: producer surplus (PS) = TR - VC.

P1

Q1

producer receives revenue greater than VC.

Difference between TR and VC provides a measure of producer well-being.

In the diagram above, the PS from selling Q1 units at P1 per unit is equal to the triangle A.

A

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Topic 1(b): Review of Producer Theory

ii. Measuring producer well-being using the supply curve.

• More common measure of producer well-being is profit ().– What is the relationship between PS and ?

• Recall:

PS = TR - VC; and

= TR - TC

= TR - VC - FC

PS = PS - FC

or PS = + FC.

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Topic 1(b): Review of Producer Theory

• Recall that CS measures the NB to consumers from consuming.

• Similarly, we can think about PS as telling us about the NB to producers from producing.

• That is, tells us how much better off the firm is by choosing Q>0.

• If Q = 0, TR=0 and TC=FC. = -FC.

• If Q>0, TR>0 and TC=FC+VC. = PS - FC.

• Tells us that maximizing is equivalent to maximizing PS.

• So even though is the “true” measure of firm well-being, we can use PS instead.

as Q = PS as Q

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Topic 1(b): Review of Producer Theoryiii. Deriving aggregate supply from individual firm supply

P

QA

Suppose two firm - A and B - each with S curves drawn below.

At $1, A supplies 2 and B supplies 3.

3

3

We are horizontally aggregating individual firm supplies to get aggregate supply.

SA

QB

7

SB

102 3 5

Aggregate S

1

Aggregate supply at $1 therefore equals 2 + 3 = 5.

At $3, A supplies 3, B supplies 7, and agg. S = 3 + 7 = 10.

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Topic 1(c): Review of Equilibrium• Review: Equilibrium.

– Brings together the producer & consumer sides of the market.

• Definition of equilibrium:

– A state of balance or rest.

– A state where there is no tendency for change.

• In the demand/supply model, equilibrium is where:

– Each consumer is choosing the best Q, given P.

• i.e, Q that maximizes CS.

– Each producer is choosing the best Q, given P.

• i.e, Q that maximizes PS.

– Prices such that consumer & producer behavior are consistent.

• usually means supply = demand

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Topic 1(c): Review of Equilibrium• Example: take the S and D curves illustrated

Q1

P1

P

Q

S

D

At price P1 consumers want to buy Q1 units, producers want to sell Q1 units consumer and producer behavior is consistent.

If P > P1, S > D and there would be pressure on P to fall.

At equilibrium of P1 and Q1, NB to consumers = CS = area A and NB to producers = PS = area B.

Aggregate NB = CS + PS = A + B

A

B

Note that area A is aggregate CS and area B is aggregate PS.

That is, CS is sum of all individual consumers’ CS and PS is sum of all individual producers’ PS.

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Topic 1(c): Review of Equilibrium

Summary:

• We have seen that :– Consumers choose Q such that P = MB

• i.e., choose to consume where P cuts D curve.• NB to consumers = CS.

– Producers choose Q such that P = MC • i.e. choose to produce where P line cuts S curve.• NB to producers = PS.

– Producer and consumer decisions are such that S=D

• Aggregate NB = sum of individual NB • Sum of individual NB = CS + PS (if consumers

and producers are the the only agents affected by the market).