1. MICROECONOMICS Principles and Analysis Frank Cowell
Exercise 3.3
MICROECONOMICS
Principles and Analysis
Frank Cowell
November 2006

2. Ex 3.3(1) Question purpose: to derive competitive supply function
method: derive AC, MC

3. 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

4. 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 :

5. Ex 3.3(1): Supply by a single firm
Average cost p
Marginal cost
Supply of output q qi

6. Ex 3.3(2) Question
purpose: to demonstrate possible absence of equilibrium
method: examine discontinuity in supply relationship

7. Ex 3.3(2): Equilibrium?  AC MC
AC,MC and supply of firm p
Demand, low value of b
Demand, med value of b
Demand, high value of b AC
Solution for high value of b is where Supply = Demand
Supply (one firm)  MC qi

8. Ex 3.3(2) Equilibrium Outcome for supply by a single price-taking firm
High demand: unique equilibrium on upper part of supply curve
Low demand: equilibrium with zero output
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

9. Ex 3.3(3) Question purpose: to demonstrate effect of averaging
method: appeal to a continuity argument

10. Ex 3.3(3) Average supply, N firms
Define average output
Set of possible values for average output:
Therefore the average supply function is

11. 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

12. Ex 3.3(3): Average supply by N firms
Average cost (for each firm) p
Marginal cost (for each firm)
Supply of output for averaged firms q q 

13. Ex 3.3(4) Question purpose: to find equilibrium in large-numbers case
method: re-examine small-numbers case

14. Ex 3.3(4) Equilibrium
Equilibrium depends on where demand curve is located
characterise in terms of (price, average output)
High demand
equilibrium is at (p, p/a) where p = aA / [a+b]
Medium demand
equilibrium is at (p, [A – p]/b)
equivalent to (p, bq) where b := a[A – p] / [bp]
Achieve this with a proportion b at q and 1–b at 0
Low demand
equilibrium is at (p, 0)

15. Ex 3.3(4): Eqm (medium demand)
AC and MC (for each firm) p
Supply of output (averaged)
Demand
Equilibrium
Equilibrium achieved by mixing firms at 0 and at q
1b here
b here q* q q 

16. Ex 3.4: Points to remember Model discontinuity carefully
Averaging may eliminate discontinuity problem in a large economy
depends whether individual agents are small.
Equilibrium in averaged model may involve identical firms doing different things
equilibrium depends on the right mixture