Frank C

owell:

Frank C

owell: M

icroeconomics

Microeconom

ics

Exercise 3.3

MICROECONOMICSMICROECONOMICSPrinciples and AnalysisPrinciples and Analysis

Frank CowellFrank Cowell

November 2006 November 2006

Frank C

owell:

Frank C

owell: M

icroeconomics

Microeconom

ics

Ex 3.3(1) Question

purposepurpose: to derive competitive supply function: to derive competitive supply function methodmethod: derive AC, MC : derive AC, MC

Frank C

owell:

Frank C

owell: M

icroeconomics

Microeconom

ics

Ex 3.3(1) Costs

Total cost is: F0 + ½ aqi2

Marginal cost: aqi

Average cost: F0/qi + ½ aqi

Therefore MC intersects AC where:

This is at output level q where:

At this point AC is at a minimum p where:

For q below q there is IRTS and vice versa

Frank C

owell:

Frank C

owell: M

icroeconomics

Microeconom

ics

Ex 3.3(1) Supply

If p > p the firm supplies an amount of output such that p = MC

If p < p the firm supplies zero output otherwise the firm would make a loss

If p = p the firm is indifferent between supplying 0 or q in either case firm makes zero profits

To summarise the supply curve consists of :

Frank C

owell:

Frank C

owell: M

icroeconomics

Microeconom

ics

Ex 3.3(1): Supply by a single firm

qi

p

Average cost

Marginal cost

Supply of output

q

Frank C

owell:

Frank C

owell: M

icroeconomics

Microeconom

ics

Ex 3.3(2) Question

purposepurpose: to demonstrate possible absence of equilibrium: to demonstrate possible absence of equilibrium methodmethod: examine discontinuity in supply relationship : examine discontinuity in supply relationship

Frank C

owell:

Frank C

owell: M

icroeconomics

Microeconom

ics

Ex 3.3(2): Equilibrium?

AC

MC

qi

p

AC,MC and supply of firm

Demand, low value of b

Demand, high value of b

Supply

(one firm)

Solution for high value of b is where Supply = Demand

Demand, med value of b

Frank C

owell:

Frank C

owell: M

icroeconomics

Microeconom

ics

Ex 3.3(2) Equilibrium

Outcome for supply by a single price-taking firm1. High demand: unique equilibrium on upper part of supply curve

2. Low demand: equilibrium with zero output

3. In between: no equilibrium

Given case 1 “Supply = Demand” implies

This implies:

But for case 1 we need p ≥ p from the above this implies

Frank C

owell:

Frank C

owell: M

icroeconomics

Microeconom

ics

Ex 3.3(3) Question

purposepurpose: to demonstrate effect of averaging: to demonstrate effect of averaging methodmethod: appeal to a continuity argument : appeal to a continuity argument

Frank C

owell:

Frank C

owell: M

icroeconomics

Microeconom

ics

Ex 3.3(3) Average supply, N firms

Define average output

Set of possible values for average output:

Therefore the average supply function is

Frank C

owell:

Frank C

owell: M

icroeconomics

Microeconom

ics

Ex 3.3(3) Average supply, limit case

As N the set J(q) becomes dense in [0, q]

So, in the limit, if p = p average output can take any value in [0, q]

Therefore the average supply function is

Frank C

owell:

Frank C

owell: M

icroeconomics

Microeconom

ics

Ex 3.3(3): Average supply by N firms

p

Average cost (for each firm)

Marginal cost (for each firm)

Supply of output for averaged firms

q q

Frank C

owell:

Frank C

owell: M

icroeconomics

Microeconom

ics

Ex 3.3(4) Question

purposepurpose: to find equilibrium in large-numbers case: to find equilibrium in large-numbers case methodmethod: re-examine small-numbers case : re-examine small-numbers case

Frank C

owell:

Frank C

owell: M

icroeconomics

Microeconom

ics

Ex 3.3(4) Equilibrium

Equilibrium depends on where demand curve is locatedcharacterise in terms of (price, average output)

High demandequilibrium is at (p, p/a) where p = aA / [a+b]

Medium demandequilibrium is at (p, [A – p]/b)equivalent to (p, q) where := a[A – p] / [bp]Achieve this with a proportion at q and 1– at 0

Low demand equilibrium is at (p, 0)

Frank C

owell:

Frank C

owell: M

icroeconomics

Microeconom

ics

Ex 3.3(4): Eqm (medium demand)

p

AC and MC (for each firm)Supply of output (averaged)

q

Demand

Equilibrium

q*

Equilibrium achieved by mixing firms at 0 and at q

here here1 here1 here

q

Frank C

owell:

Frank C

owell: M

icroeconomics

Microeconom

ics

Ex 3.4: Points to remember

Model discontinuity carefullyModel discontinuity carefully Averaging may eliminate discontinuity problem in Averaging may eliminate discontinuity problem in

a large economya large economy depends whether individual agents are small.depends whether individual agents are small.

Equilibrium in averaged model may involve Equilibrium in averaged model may involve identical firms doing different thingsidentical firms doing different things equilibrium depends on the right mixtureequilibrium depends on the right mixture