Transcript Extensive Form - London School of Economics

Frank Cowell: EC202 Microeconomics
May 2008
Revision Lecture 1
EC202: Microeconomic Principles II
Frank Cowell
Frank Cowell: EC202 Microeconomics
Objectives of the lecture
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A look back at Term 1
Introduction to exam preparation
Reference materials used (1)
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exam papers (and outline answers)
2003 1(c)
2004 1(c)
2005 1(a)
2006 1(a)
2007 1(a)
Reference materials used (2)
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CfD presentations 2.9
related to past exam question
(...more to follow next week)
Frank Cowell: EC202 Microeconomics
Principles
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Scope of exam material
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Resit
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syllabus for 2007/8 is same as 2006/7
so resit candidates from last year get the same paper as new candidates
Structure and format of paper
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what’s covered in the lectures…
… is definitive for the exam
follows that of last three years
check out the rubric from, say, 2007 paper
Mark scheme
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40 marks for question 1 (8 marks for each of the five parts)
20 marks for each of the other three questions
multipart questions: except where it’s obvious, roughly equal marks across parts
Frank Cowell: EC202 Microeconomics
Question Style – three types
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1 Principles
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2 Model solving
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a standard framework
you just turn the wheels
3 Model building
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reason on standard results and arguments
can use verbal and/or mathematical reasoning
usually get guidance in the question
longer question sometimes easier?
Examples
from past
question 1
One type not necessarily “easier” or “harder” than another
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get you to display different skills
part A (question 1) usually gets you to do both types 1 and 2
type 3 usually only in parts B and C of paper
Frank Cowell: EC202 Microeconomics
2004 1(c)
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Straightforward
“principles” question
Just say what you need
to say
Frank Cowell: EC202 Microeconomics
2005 1(a)
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Straight “principles”
Note contrast between
firm and consumer
Be sure to give your
reasons
Frank Cowell: EC202 Microeconomics
2006 1(a)
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Principles again
But format of question
gives you a hint…
…write out
decomposition formula
Then read off results
Frank Cowell: EC202 Microeconomics
2003 1(c)
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A model-solving
question
(i) just set E(r) = 0 and
twiddle
(ii) check what
happens to E if you
change r
(iii) draw diagram and
reason
Frank Cowell: EC202 Microeconomics
2007 1(a) – question and approach
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A “hybrid”
question
Mainly modelsolving
But there’s an
important principle
will a solution even
exist?
What’s the solution to the monopolist’s problem?
Approach:
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Find the expression for profits
Then try to maximise…
Frank Cowell: EC202 Microeconomics
2007 1(a) – main answer
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To get profits we
need demand
function
You could just
jump to last line
Now write down
profit expression
Note wording in
last line
Frank Cowell: EC202 Microeconomics
2007 1(a) – finishing off answer
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Use knowledge of
basic principles
Effectively the
competitive case
No solution!
(we covered this in
lectures)
Frank Cowell: EC202 Microeconomics
Long questions
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Let’s look at an example
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Illustrates type 2 question
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taken from exercise in the book
but of “exam type” difficulty
covered in CfD
Ex 2.9 is mainly model solving
next week: look at model building
Look out for tips
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Use simple principles to give you a shortcut to the answer
Use pictures where they help
Frank Cowell: EC202 Microeconomics
Ex 2.9(1): Question
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purpose: demonstrate relationship between short and long run
method: Lagrangean approach to cost minimisation. First part can be solved by
a “trick”
Frank Cowell: EC202 Microeconomics
Ex 2.9(1): Long-run costs
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Production function is homogeneous of degree 1
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CRTS implies constant average cost
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increase all inputs by a factor t > 0 (i.e. z → tz)…
…and output increases by the same factor (i.e. q → tq)
constant returns to scale in the long run
C(w, q) / q = A (a constant)
so C(w, q) = Aq
differentiating: Cq(w, q) = A
So LRMC = LRAC = constant
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Their graphs will be an identical straight line
Frank Cowell: EC202 Microeconomics
Ex 2.9(2): Question
method:
 Standard Lagrangean approach
Frank Cowell: EC202 Microeconomics
Ex 2.9(2): short-run Lagrangean
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In the short run amount of good 3 is fixed
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z3 = `z3
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Could write the Lagrangean as
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But it is more convenient to transform the problem thus
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where
Frank Cowell: EC202 Microeconomics
Ex 2.9(2): Isoquants
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Sketch the isoquant map
z2
z1
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Isoquants do not touch the axes
So maximum problem must have an interior solution
Frank Cowell: EC202 Microeconomics
Ex 2.9(2): short-run FOCs
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Differentiating Lagrangean, the FOCS are
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This implies
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To find conditional demand function must solve for l
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use the above equations…
…and the production function
Frank Cowell: EC202 Microeconomics
Ex 2.9(2): short-run FOCs (more)
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Using FOCs and the production function:
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This implies
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where
This will give us the short-run cost function
Frank Cowell: EC202 Microeconomics
Ex 2.9(2): short-run costs
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By definition, short-run
costs are:
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This becomes
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Substituting for k:
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From this we get
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SRAC:
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SRMC:
Frank Cowell: EC202 Microeconomics
Ex 2.9(2): short-run MC and AC
marginal
cost
average
cost
q
Frank Cowell: EC202 Microeconomics
Ex 2.9(3): Question
method:
 Draw the standard supply-curve diagram
 Manipulate the relationship p = MC
Frank Cowell: EC202 Microeconomics
Ex 2.9(3): short-run supply curve
average cost curve
marginal cost curve
minimum average cost
p
supply curve
p
q
q
Frank Cowell: EC202 Microeconomics
Ex 2.9(3): short-run supply elasticity
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Use the expression for marginal cost:
Set p = MC for p ≥ p
Rearrange to get supply curve
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Differentiate last line to get supply elasticity
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Frank Cowell: EC202 Microeconomics
Ex 2.9: Points to remember
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Exploit CRTS to give you easy results
Try transforming the Lagrangean to make it easier to
manipulate
Use MC curve to derive supply curve
Frank Cowell: EC202 Microeconomics
Next time
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Think more about method for long questions
Look at a few CfD
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4.12, 4.13
5.1
7.8
9.6
See how they illustrate method
Connect these to past exam questions