Transcript Microeconomics (draft slides) - Civil and Environmental Engineering

Civil Systems Planning
Benefit/Cost Analysis
Scott Matthews
12-706/19-702 / 73-359
Lecture 7 - Microecon Recap
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Discussion - “willingness to pay”
Survey of students of WTP for beer
How much for 1 beer? 2 beers? Etc.
Does similar form hold for all goods?
What types of goods different?
Economists also refer to this as demand
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(Individual) Demand Curves
 Downward Sloping is a result of diminishing marginal
utility of each additional unit (also consider as WTP)
 Presumes that at some point you have enough to
make you happy and do not value additional units
Price
A
Actually an inverse
demand curve (where
P = f(Q) instead).
B
P*
0
1
2
3
4
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Q*
Quantity
3
Market Demand
Price
A
A
B
B
P*
P*
0
1
2
3
4
Q
0
1
2
3
4
5 Q
If above graphs show two (groups of) consumer
demands, what is social demand curve?
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Market Demand
P*
0
1
2
3
4
5
6
7
8
9 Q
Found by calculating the horizontal sum of
individual demand curves
Market demand then measures ‘total
and 73-359 market’
consumer surplus12-706
of entire
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Social WTP (i.e. market demand)
Price
A
B
P*
0
1
2
3
4
Q*
Quantity
‘Aggregate’ demand function: how all potential
consumers in society value the good or service
(i.e., someone willing to pay every price…)
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This is the kind of demand
curves we care about 6
First: Elasticities of Demand
Measurement of how “responsive”
demand is to some change in price or
income.
Slope of demand curve = Dp/Dq.
Elasticity of demand, e, is defined to be
the percent change in quantity divided by
the percent
change in price.
Dq
e
q
Dp
p

pDq
qDp
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Elasticities of Demand
Elastic demand: e > 1.
If P inc. by 1%, demand dec. by more than 1%.
Unit elasticity: e = 1. If P inc. by 1%, demand dec. by 1%.
Inelastic demand: e < 1
If P inc. by 1%, demand dec. by less than 1%.
P
P
Q
Q
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Elasticities of Demand
P
Necessities, demand is
Completely insensitive
To price
Perfectly
Inelastic
P
Q
Perfectly
Elastic
A change in price causes
Demand to go to zero
(no easy examples)
Q
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Elasticity - Some Formulas
Point elasticity = dq/dp * (p/q)
For linear curve, q = (p-a)/b so dq/dp = 1/b
Linear curve point elasticity =(1/b) *p/q =
(1/b)*(a+bq)/q =(a/bq) + 1
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Sorta Timely Analysis
How sensitive is gasoline demand to price
changes?
Historically, we have seen relatively little change
in demand. Recently?
New AAA report: higher gasoline prices have
caused a 3 percent reduction in demand from a
year ago.
What was Dp? Dq? e?
What does that tell us about gasoline?
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Maglev System Example
Maglev - downtown, tech center, UPMC,
CMU
20,000 riders per day forecast by
developers.
Let’s assume:
price elasticity -0.3;
linear demand;
20,000 riders @ average fare of $ 1.20.
Estimate Total Willingness to Pay.
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Example calculations
We have one point on demand curve:
1.2 = a + b*(20,000)
We know an elasticity value:
elasticity for linear curve = 1 + a/bq
-0.3 = 1 + a/b*(20,000)
Solve with two simultaneous equations:
a = 5.2
b = -0.0002 or 2.0 x 10^-4
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Types of Costs - from 3-03
Private - paid by consumers
Social - paid by all of society
Opportunity - cost of foregone options
Fixed - do not vary with usage
Variable - vary directly with usage
External - imposed by users on non-users
e.g. traffic, pollution, health risks
Private decisions usually ignore external
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Making Cost Functions
Fundamental to analysis and policies
Three stages:
 Technical knowledge of alternatives
 Apply input (material) prices to options
 Relate price to cost
Obvious need for engineering/economics
Main point: consider cost of all parties
Included: labor, materials, hazard costs
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Functional Forms
TC(q) = F+ VC(q)
Use TC eq’n to generate unit costs
Average Total: ATC = TC/q
Variable: AVC = VC/q
Marginal: MC = [TC]/  q = DTCDq
but  F/  q = 0, so MC = [VC]/  q
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Short Run vs. Long Run Cost
Short term / short run - some costs fixed
In long run, “all costs variable”
Difference is in ‘degree of control of plans’
Generally say we are ‘constrained in the
short run but not the long run’
So TC(q) < = SRTC(q)
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Firm Production Functions
MC
What do marginal,
Average cost curves
Tell us?
Variable cost shows
Non-fixed components
Of producing the good
P
AVC
Marginal costs show us
Cost of producing one
Additional good
Q
Where would firm produce?
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BCA Part 2: Cost
Welfare Economics Continued
The upper segment of a firm’s marginal cost curve corresponds
to the firm’s SR supply curve. Again, diminishing returns occur.
Price
At any given price, determines
how much output to produce to
maximize profit
Supply=MC
AVC
Quantity
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Supply/Marginal Cost Notes
Demand: WTP for each additional unit
Supply: cost incurred for each additional unit
Price
At any given price, determines
how much output to produce to
maximize profit
Supply=MC
P*
Q1
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Q* Q2
Quantity
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Supply/Marginal Cost Notes
Recall: We always want to be considering opportunity costs
(total asset value to society) and not accounting costs
Price
Area under MC is TVC - why?
Supply=MC
P*
Q1
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Q* Q2
Quantity
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Unifying Cost and Supply
Economists learn “Supply and Demand”
Equilibrium (meeting point): where S = D
In our case, substitute ‘cost’ for supply
Why cost? Need to trade-off Demand
Using MC is a standard method
Recall this is a perfectly competitive world!
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Example
Demand Function: p = 4 - 3q
Supply function: p = 1.5q
Assume equilibrium, what is p,q?
In eq: S=D; 4-3q=1.5q ; 4.5q=4 ; q=8/9
P=1.5q=(3/2)*(8/9)= 4/3
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Pricing Strategies
 Highway pricing
If price set equal to AC (which is assumed to be TC/q then at q,
total costs covered
p ~ AVC: manages usage of highway
p = f(fares, fees, travel times, discomfort)
Price increase=> less users (BCA)
MC pricing: more users, higher price
What about social/external costs?
Might want to set p=MSC
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Estimating Linear Demand
Functions
 As above, sometimes we don’t know demand
 Focus on demand (care more about CS) but can use
similar methods to estimate costs (supply)
 Ordinary least squares regression used
minimize the sum of squared deviations between estimated line
and p,q observations: p = a + bq + e
Standard algorithms to compute parameter estimates spreadsheets, Minitab, S, etc.
Estimates of uncertainty of estimates are obtained (based upon
assumption of identically normally distributed error terms).
 Can have multiple linear terms
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Log-linear Function
 q = a(p)b(hh)c…..
 Conditions: a positive, b negative, c positive,...
 If q = a(p)b : Elasticity interesting = (dq/dp)*(p/q) =
abp(b-1)*(p/q) = b*(apb/apb) = b.
Constant elasticity at all points.
 Easiest way to estimate: linearize and use ordinary least
squares regression (see Chap 12)
E.g., ln q = ln a + b ln(p) + c ln(hh) ..
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Log-linear Function
q = a*pb and taking log of each side gives: ln q =
ln a + b ln p which can be re-written as q’ = a’ +
b p’, linear in the parameters and amenable to
OLS regression.
This violates error term assumptions of OLS
regression.
Alternative is maximum likelihood - select
parameters to max. chance of seeing obs.
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Maglev Log-Linear Function
q = apb - From above, b = -0.3, so if p =
1.2 and q = 20,000; so 20,000 = a*(1.2)-0.3
; a = 21,124.
If p becomes 1.0 then q = 21,124*(1)-0.3 =
21,124.
Linear model - 21,000
Remaining revenue, TWtP values similar
but NOT EQUAL.
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Demand Example (cont)
Maglev Demand Function:
p = 5.2 - 0.0002*q
Revenue: 1.2*20,000 = $ 24,000 per day
TWtP = Revenue + Consumer Surplus
TWtP = pq + 1/2*(a-p)q = 1.2*20,000 +
0.5*(5.2-1.2)*20,000 = 24,000 + 40,000 =
$ 64,000 per day.
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Change in Fare to $ 1.00
 From demand curve: 1.0 = 5.2 - 0.0002q, so q becomes
21,000.
Using elasticity: 16.7% fare change (1.2-1/1.2), so q would
change by -0.3*16.7 = 5.001% to 21,002 (slightly different value)
 Change to Revenue = 1*21,000 - 1.2*20,000 = 21,000 24,000 = -3,000.
 Change CS = 0.5*(0.2)*(20,000+21,000)= 4,100
 Change to TWtP = (21,000-20,000)*1 + (1.2-1)*(21,00020,000)/2 = 1,100.
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