Economics of Regulation
Pricing Issues
Ramsey Pricing (Viscusi p. 365)
A. Value-of-service pricing or optimal pricing with
a break-even constraint
B. Maximize total surplus with the constraint that
the firm must break-even.
Ramsey Pricing (Viscusi p. 365)
C. Welfare will be maximized when prices exceed
marginal production costs in direct proportion to the
value buyers attach to a particular good or service, varies
inversely with buyers' elasticity of demand.
Where Pi = price of good i; MCi = marginal cost of good i; ei = elasticity
of demand of good I; λ= constant. This is the same as cutting the
output of all goods by the same proportion from the P=MC point until
the revenue just equals total cost.
Ramsey Pricing (Viscusi p. 365)
D. Example - Two product Natural Monopoly
1. Total Cost: C=1800 + 20X + 20Y
2. Market Demand for goods X and Y are
X=100-Px
Y=120-2Py
Demands are independent
3. MCx=MCy=20; Marginal cost pricing covers variable costs
but not 1800
4. So how do we cover the 1800? Increase the price by the
same proportion!
P=36.1; X=63.9; Y=47.7; TR=TC=4032
Ramsey Pricing (Viscusi p. 365)
DFH and JKH are deadweight loss. Area of triangle
1/2hb. 1/2(16.1)(32.3) + ½ (16.1)(16.1) = 260+130=390
Ramsey Pricing (Viscusi p. 365)
5. It's better to raise the price of X more than the
price of Y. X is more inelastic and results in less
deadweight loss. Cutting output by the same
proportion until total revenue equals total cost
yields Px=40 Py=30 X=Y=60 TR =2400+1800=
4200; TC = 1800+1200+1200=4200.
Ramsey Pricing (Viscusi p. 365)
Ramsey Pricing (Viscusi p. 365)
DWL = ½ (20)(20) + ½ (10)(20) = 200 + 100 = 300
which is less than 390.
ASIDE: How would you figure out Lambda?
(P-MC)/P=Lambda/e, so (40-20)/40 = Lambda / e, e
= -1 * 40/60 or -2/3, Lambda = -1/3
Verify for good Y
e=-2*30/60=-1, (30-20)/30=Lambda/e, Lambda = 1/3
Peak Load Pricing (Viscusi p. 396)
A. Electric Utility
– 1. Too costly (or impossible) to store electricity.
– 2. Therefore, they must have enough capacity to
supply demand at all times. Capacity is determined
by peak demand.
Peak Load Pricing (Viscusi p. 396)
• 3. To minimize total cost, electric companies
supply a variety of different plant types
– a. Nuclear plants have relatively low variable or
"running" costs and high fixed costs. These are
used as base load plants - run as many hours as
possible.
– b. Combustion turbines have relatively high
running costs but low fixed costs. These are used
as peak-load plants - only run during times of high
demand.
Peak Load Pricing (Viscusi p. 396)
B. Peak Load pricing problem - assume only base load plants for
simplicity.
Peak Load Pricing (Viscusi p. 396)
With this type of demand, it is efficient to price off
peak at b and peak at b + where is the capacity
charge. SRMC=LRMC=Peak demand when
capacity is at efficient levels. If this is not the
case and peak demand is higher at say peak'.
Then there is a deadweight loss and the firm can
expand capacity to K* to capture the DWL.
Peak Load Pricing (Viscusi p. 396)
Peak Load Pricing (Viscusi p. 396)
Peak Load Pricing (Viscusi p. 396)
C. Single Price - Suppose you have a single price.
D. Peak-shifting - One would think that the optimal
solution is to charge peak demanders b+ and off
peak b. However this may result in peak-shifting if
the demands are close together. Consider the
case where b=0.
Peak Load Pricing (Viscusi p. 396)
In this case, the Peak demand (R) is less than the off-peak
demand (S). This doesn't make sense, since you are charging
capacity costs to those who use less capacity.
Peak Load Pricing (Viscusi p. 396)
E. Peak-shifting solution
Construct a demand for capacity curve (think of
capacity as a non-rival public good that both can
use) by adding the two demand curves. Optimal K
is where LRMC = Demand for capacity. Then find
the peak price on the peak demand curve and the
off-=peak price on the off-peak curve.
Peak Load Pricing (Viscusi p. 396)
Two-part Tariffs (Viscusi p. 362)
A. Def. - a non-linear price consisting of a
fixed fee regardless of consumption and a
price per unit. It is possible to have
efficient pricing if P=MC and fixed fee
covers the loess of a natural monopoly (See
Natural Monopoly Graph)
B. Fixed Fee = loss/(# of customers)
Two-part Tariffs (Viscusi p. 362)
C. Problems
• 1. Because customers differ, fixed fee may
exceed their individual consumer surplus and
drive them from the market (i.e. telephone
service)
• 2. This is an efficiency loss since they would
have paid the MC.
Two-part Tariffs (Viscusi p. 362)
D. Solution
• 1. Charge different fixed fees to different
customers (i.e. res vs. bus.)
E. Optimal two-part tariff comes from
balancing efficiency losses due to losing
customers from a fixed fee against
increased consumption losses as
price/unit increases above MC.