ec202: worked example #3.4
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EC202: Worked Example #3.4. Frank Cowell April 2003. T his presentation covers exactly the material set out in the file WorkedExamples.pdf, but with the addition of a few graphics and comments To start the presentation select S lideshow\ V iew Show or click on icon below left. - PowerPoint PPT PresentationTRANSCRIPT
EC202: Worked Example #3.4
Frank CowellApril 2003
•This presentation covers exactly the material set out in the file WorkedExamples.pdf, but with the addition of a few graphics and comments
•To start the presentation select Slideshow\View Show or click on icon below left.
• Mouse click or [Enter] to advance through slide show
WX3.4: Monopoly and competition
Part 1: Competition
WX3.4: Find Firm’s Supply Curve
Integrate MC in the question to get total costs
Divide by Q to get average costs
Differentiate to find minimum AC at
Where average costs are:
Given a price can then find output from supply curve
WX3.4: The Firm’s Supply Curve
P
average cost
a+bQmarginal cost
F/Q+a+0.5bQ
P - a——
bQ*=
Psupply curve
WX3.4: Monopoly and competition
Part 2: Unregulated monopoly
WX3.4: Find monopolist’s equilibrium
Given the demand curve (AR), total revenue is
So, MR is
FOC for the monopolist (MR=MC) is
Solving for Q we get
And from this we have
WX3.4: Monopolist’s equilibrium
F/Q+a+0.5bQ
Q
average revenue
average cost
a+bQmarginal
cost
A - 0.5bQ
P
Q**
P**
c**
marginal revenue
A - bQ
WX3.4: Monopoly and competition
Part 3: Regulated monopoly
WX3.4: Introduce price ceiling
A price ceiling alters the effective demand curve
So AR is now:
Multiply by Q and then differentiate to get MR:
Note that MR is discontinuous, exactly where AR is kinked
Effect of price ceiling depends on position of MC relative to this discontinuity
WX3.4: effect of high price ceiling
Q
marginal revenue
average revenue
marginal cost
P
Q**
P**
c**
Pmax
Q0
(Output unchanged)
WX3.4: effect of low price ceiling
Q
marginal revenue
average revenue
marginal cost
P
Q**
P**
c**Pmax
Q0
(Output falls)
WX3.4: effect of intermediate price ceiling
Q
marginal revenue
average revenue
marginal cost
P
Q**
P**
c**Pmax
Q0
(Output rises to Q0)
WX3.4: intermediate price ceiling (2)
Q
marginal revenue
average revenue
marginal cost
P
Q**
P**
c**Pmax
Q0
(Output rises)
WX3.4: Points to remember
• Make good use of a helpful diagram to “see” the problem
• Re-use the solution to one part of the problem to build the next.
• Don’t be fazed by the presence of a discontinuity – everything is nice and regular either side of it.