1. MICROECONOMICS Principles and Analysis Frank Cowell
Exercise 3.4
MICROECONOMICS
Principles and Analysis
Frank Cowell
November 2006

2. Ex 3.4(1) Question purpose: to derive competitive supply function
method: derive AC, MC

3. Ex 3.4(1) Costs Integrate MC to get total cost
Divide by q to get average costs
Differentiate to find minimum AC at
Average costs at this point are
If price is above this level find equilibrium where price = MC:
Solving this we get

4. Ex 3.4(1): Firm’s supply curve
Average cost
Marginal cost
Supply of output
Relation between price and output
a+bq P p
F0/q+a+0.5bq q
p  a —— b
q*= q

5. Ex 3.4(2) Question purpose: to derive monopolist’s solution
method: derive AR, MR

6. Ex 3.4(2) Monopolist’s equilibrium
Given the demand curve total revenue is Aq  ½Bq2
So, MR is
Monopolist’s FOC (MR=MC)
Solving for q we get
And from this we have

7. Ex 3.4(2): Monopoly output and price
AC and MC curves
Demand (average revenue)
Marginal revenue
Profit-maximising output
a+bq
MC and price at q**
p**
F0/q+a+0.5bq
c**
A  0.5bq
A  bq q
q**

8. Ex 3.4(3) Question purpose: to derive modified monopoly solution
method: derive modified AR, MR – watch out for discontinuity!

9. Ex 3.4(3) Regulated monopolist
Price ceiling alters the effective demand curve
So AR is now:
Multiply by q and then differentiate to get MR:
MR is discontinuous, exactly where AR is kinked
Effect of price ceiling depends on position of MC relative to this discontinuity

10. Ex 3.4(3): High price ceiling
AC and MC curves
Demand (average revenue)
Marginal revenue
Profit-maximising output
MC and price at q**
p**
A high ceiling has no effect on equilibrium
c** q
q**

11. Ex 3.4(3): Low price ceiling
AC and MC curves
Demand (average revenue)
Marginal revenue
Profit-maximising output
p**
A low ceiling yields equilibrium at reduced output q1
price = MC = price ceiling
c** q q1
q** q0

12. Ex 3.4(3): Medium price ceiling (i)
AC and MC curves
Demand (average revenue)
Marginal revenue
Profit-maximising output
p**
A medium ceiling yields equilibrium at increased output q2
c** q
q** q2 q0

13. Ex 3.4(3): Medium price ceiling (ii)
AC and MC curves
Demand (average revenue)
Marginal revenue
Profit-maximising output
p**
Again, a medium ceiling yields equilibrium at increased output q0
c** q0 q
q**

14. Ex 3.4: Points to remember
Make good use of a diagram to “see” the problem
Re-use the solutions
one part of the problem…
…helps to build the next.
Don’t be fazed by the presence of a discontinuity
everything is nice and regular either side of it.