Exercise 3.3
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Transcript of Exercise 3.3
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Frank C
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icroeconomics
Microeconom
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Exercise 3.3
MICROECONOMICSMICROECONOMICSPrinciples and AnalysisPrinciples and Analysis
Frank CowellFrank Cowell
November 2006 November 2006
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Frank C
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icroeconomics
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Ex 3.3(1) Question
purposepurpose: to derive competitive supply function: to derive competitive supply function methodmethod: derive AC, MC : derive AC, MC
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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
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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 :
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Ex 3.3(1): Supply by a single firm
qi
p
Average cost
Marginal cost
Supply of output
q
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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
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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
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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
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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
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Ex 3.3(3) Average supply, N firms
Define average output
Set of possible values for average output:
Therefore the average supply function is
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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
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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
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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
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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)
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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
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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