1

Review

1. Production function

- Types of production functions

- Marginal productivity

- Returns to scale

2. The cost minimization problem

- Solution: MPL(K,L)/w = MPK(K,L)/r

- What happens when price of an input increases?

3. Deriving the cost function

- Solution to cost minimization problem

- Properties of the cost function (marginal and average costs)

2

Economic Profit

Economic profit is the difference between total revenue and the economic costs.

Difference between economic costs and accounting costs: The economic costs includethe opportunity costs.

Example: Suppose you start a business:- the expected revenue is $50,000 per year. - the total costs of supplies and labor are $35,000.- Instead of opening the business you can also work in the bank and earn $25,000 per

year.

- The opportunity costs are $25,000- The economic profit is -$10,000- The accounting profit is $15,000

3

Firm’s supply: how much to produce?

A firm chooses Q to maximize profit.

)()()(max QTCQTRQQ

The firm’s problem

Total cost of producing Q units depends on the production function and input costs.

Total revenue of is the money that the firm receives from Q units (i.e., price times the quantity sold). It depends on competition and demand

Deriving the firm’s supply

Def. A firm is a price taker if it can sell any quantity at a given price of p per unit.

0..

)(max

Qts

QTCpQQ

For a given price, the firm’s problem is to choosequantity to maximize profit.

Optimality condition: P = MC(Q)

How much should a price taking firm produce?

Profit Maximization

Optimality condition:1. P = MC(Q)2. MC(Q) increases

Short Run Supply

Example. A firm has the cost function TC(Q) = 100 + 20Q + Q2 and can sell each unit for a price of 30. How many units will it sell? What is the profit?

Calculate the firm’s profit if the market price is 40, 20, 15. Derive the firm’s supply.

Short Run Supply

A firm has the cost function TC(Q) = 100 + 20Q + Q2:

TFC = 100 ATC(Q)=100/Q+20+Q TVC(q) = 20Q + Q2

AVC(q) = 20 + Q MC(q) = 20 + 2Q

The firm’s short run supply curve is:

- If the price is P < 20: then the firm produces nothing Q = 0

- If price is P > 20: then P = MC(Q) P = 20+2Q Q =𝑝−20

2

Q

$

AVC

ATC

SMC

ps20

8

Short Run Supply

Q

$

AVC

ATC

SMC

ps20

Supply

The firm’s short run supply curve is:

- If the price is P < 20: then the firm produces nothing Q = 0

- If price is P > 20: then P = MC(Q) P = 20+2Q Q =𝑝−20

2

The Firm’s Decision

Does the firm choose to produce a positive quantity Q>0 or to shut down and produce nothing Q=0?

𝑝𝑠 = 𝑚𝑖𝑛𝑄𝐴𝑉𝐶(𝑄)

Short Run Supply

The firm’s supply:If P < Ps, the firm produces nothing, Q=0

If P > Ps, the firm produces Q>0 such that MC(Q)=p

Quantity

$

AVCATC

SMC

Ps

Fixed costs are sunk:

Key Definition: A single firm’s Short run supply curve specifies the profitmaximizing output for each market price.

The Firm’s Decision

)()()(max QTCQTRQQ

The firm’s problem

Optimality condition:If MR(Q)> MC(Q), the firm’s profit increases if it produces more output.If MR(Q) < MC(Q), the firm’s profit decreases if it produces more output.

The profit maximization condition is MR(Q) = MC(Q) Since the firm is a price taker: p=MR(Q)=MC(Q) We must also check the shut-down condition: p>MinAVC(Q)

Short Run Supply

Important to remember:if the firm produces output Q and sells it for a price p then:

1. When p>ATC(Q) the firm makes a profit. When p<ATC(Q) the firm loses money

2. When p>AVC(Q) the firm produces Q>0, when p<AVC(Q) the firm shuts down (assuming all fixed costs are sunk)

3. When AVC(Q)<p<ATC(Q) the firm operates at a loss

Short Run Market Supply Curve

Definition: The short run market supply is the sum of the quantities each firm supplies at that price.

Example: suppose 3 types of firms with different marginal costs and different shut down prices

14

Producer Surplus

Individual

supply

p

q

p*

q*

PS

The producer surplus is the monetary benefit of a producer

from a transaction= area between the supply curve and the

price.

Perfectly Competitive Market

A perfectly competitive market satisfies the following conditions:

1. Fragmented industry: consists of many small buyers and sellers.

2. Buyers and sellers are “price takers”:- Each buyer’s purchases are small and do not affect the market price.- Each seller is small and does not affect the market price.- No seller can affect the price of inputs.

3. Firms produce identical products.

4. Perfect information about prices.

5. All firms have equal access to inputs, have the same technology, and there is free entry. Implies that firms have identical long run cost functions.

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Perfectly Competitive Market

• The Law of One Price: Since products are identical and there is perfect information, there is a single price at which transactions occur.

Why? What happens if one firm sets price p and another sets p’< p?

• A single firm takes the price as given and chooses Q to maximize profit.

0..

)(max

Qts

QTCpQQ

The firm’s problem

16

Optimal solution: p=MC(Q)

Short Run Equilibrium

For a given number of firms N, a short run equilibrium is a pair of price andquantity (Q,P) such that:

1. Each producer maximizes profits given price P

2. Markets clear (aggregate supply equals aggregate demand)

Where 𝑞𝑖𝑆 𝑃 is firm i’s individual profit-maximizing output given price P.

)()(1

PQPqQ DN

i

S

i

S

17

Short Run Equilibrium Graphically

q

$

AVC

ATCSMC

ps

Typical firm

18

Supply

$

Market with n identical firms

Demand

Supply

Q

p*

q* Q*=nq*

Short Run Equilibrium: example

Suppose first that a market consists of 300 identical firms, all with the same cost curve:TC(q)= 0.1 + 150q2. Consumers’ demand is given by Qd(p) = 60 – p. (a) What is the equilibrium price and quantity? (b) Do firms make positive profits in the market equilibrium?

Step 1: Derive individual supply curve

FC = 0.1 (all are sunk, NSC= 0); AVC(q) = 150q; MC(q)=300q

Since min{AVC(q)}=0, the firm always produces q>0.

The profit maximizing condition: MC(q)=MR(q), we have that 300q=p, or qs(p) = p/300

Step 2: derive the market supply curve

Qs(p) = 300 qs(p) =300(p/300) = p

Step 3: solve for equilibrium

Qs(p)= Qd(p) or p = 60 – p so that

p1*= 30, Q* = 30 and each firm produces q1* = 30/300 = 0.1

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Short Run Equilibrium: example

(b) Do firms make positive profits at the market equilibrium?

Condition for positive profits: p* > ATC(q*)

ATC (q)= TC(q)/q = 0.1/q + 150q.

Since each firm produces q1* = 0.1, we have that ATC(q1*) = 16< 30 =

p1*, Therefore, p1* > ATC(q1*) and profits are positive

The profit of each firm is: pq-TC(q)= 30∙0.1-(0.1+150 ∙ 0.12)=1.4

20

Short Run Equilibrium: example

(c) What happens when the number of firms increases from 300 to 500?

A single firm’s supply is unchanged: MC(q)=p and qs(p) = p/300

But now, market supply increases to Q(p)=500 (p/300) and for market to clear

we have that:

500(p/300)= 60 – p or p2*=22.5 and Q2*= 37.5 and the individual firm

produces q2* = 37.5/500 =0.075

(d) Does each firm earn a profit? Condition for positive profits: ATC(q*) < p*

ATC (q2*)= 0.1/q + 150q= 0.1/0.075+150∙0.075 =12.58 < 22.5 = p2*

The profit of each firm pq-TC(q)= 22.5 ∙ 0.075-(0.1+150 ∙ 0.0752)=0.7

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Short Run Equilibrium: comparative statics

What happens when the number of firms increases?

Market supply increases, price drops, and each firm produces less.

22

Short Run Equilibrium: example 2

A town has 200 identical cafes, all with the same cost curve:TC(q)= FC+VC = 4 + 2q2. The inhabitants’ total demand for coffee is Qd(p) = 120 – 10 p. (a) What is the equilibrium price and quantity? (b) What is a single cafe’s profit? Calculate the town’s consumer, producer and total

surpluses.(c) The town’s mayor closes 160 cafes in an effort to reduce the inhabitants’ coffee

consumption. Answer (a) and (b) for n=40. How are the firms’ total profits and producer surplus related?

Answers for n=200:

p* = 2, Q* = 100, π = -3.5, CS = 500, PS = 100, TS = 600

Answers for n=40:

p* = 6, Q* = 60, π = 0.5, CS = 180, PS = 180, TS = 360, PS = n (π+FC) = 40 (0.5+4)

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24

Short Run Equilibrium: producer surplus

Demand

Individual supply

p

q

p*

q*

PS

Producer surplus = area

between the supply curve

and the price.

Profit = PS – FC (sunk)

25

Short Run Equilibrium: market surplus

Demand

Market

supply

p

Q

p*

Q*

Suppose that all firms are

identical (so linear supply).

PS

CS

In equilibrium on a perfectly

competitive market, total

surplus is maximized.