Taxes: Lump-sum (aka Head Tax) vs per-unit
Y
= $ on all
other goods
I
Y0
Per-unit tax
BL
tX *
Original Budget Line
A
Y*
Lump-Sum Tax BL
I
I
PX + t
X*
PX
Suppose that the intial price of good X is PX and a per-unit tax of $ t is put on
good X. The per-unit
Weighing Costs and Benefits
( a ) = B( a ) C( a )
Proft, or
Net Benefit
( a*) = 0
a
Benefit,
Cost
If an activity is worth pursuing
at all, it should be pursued up
to the point at which marginal
profit is zero, equivalently,
marginal benefit equals
margi
Excise Taxes and Competitive Equilibrium: Short-run
$/q
Post-tax SMC
$/Q
Demand
Post-tax Supply
Post-tax SAVC
t
P1
Pre-tax Supply
P0
SAVC
SMC
q1
q
Q1 Q0
Q
q0
Firm
Market
The bold lines on the left are a firms pre-tax SMC and SAVC , q0 the firms pre-tax ou
Optimal subsidy for a natural monopolist
$/Q
a
P*
b
AC
c
MC
d
D
s
MR
Q*
MC s
Q
The efficient output is Q* (where MC intersects D), which yields total surplus of a. An
unregulated monopolist would produce less than Q*. Suppose now we give a subsidy of s
pe
Income and Substitution Effects of an Interest Rate Increase
C2
New Budget Line
Total Effect:
A to B
Substitution Effect:
A to C
Income Effect:
C to B
Compensated
Budget Line
B
C
A
Endowment
I2
Original Budget Line
I1
C 1 = Consumption Today
Assumption: C
Monopoly: Straight-Line Demand and Constant Returns
Let the demand be given by P = A Q (for 0 < Q < A) and let the cost function be C(Q) = kQ , where k > 0.
(This firm has constant returns to scale, since long-run average cost is constant, here equal to k
First Welfare Theorem: Exchange Economy
Let X be a set of alternatives. We say that x X is Pareto Optimal if there is no other x X such that everyone
(strictly) prefers x to x.
In an exchange economy with 2 goods, X and Y , and two consumers A and B , con
Optimality in exchange:
X
B
B
Y
B
An allocation is Pareto optimal (or efficient) if there is no
other allocation that all consumers prefer. At an efficient
allocation for two consumers, the indifference curves should
just touch, but not cross anywhere ins
The DWL of an Excise Tax
Let the per-unit excise tax be $t. Let (P0, Q0) be the initial price-quantity, P s be the post-tax price to
sellers and Pb be the post-tax price to buyers, and Q1 the post-tax equilibrium quantity. Of course t = Pb
Ps. In the dia
Cost-Benefit Calculations: Excise Taxes and Price Ceilings
Let the demand curve be given by D = 30 P and the supply curve by S = 1 P , where P is measured in
2
dollars. The initial equilibrium price is $20 and the equilibrium quantity is 10. The price ela
Cost-Benefit Analysis
Benefit of Producing Q = Total Value to Consumers of Q units = Maximum Amount
Consumers would be willing to pay to consume Q units = Area under Demand Curve*
P
The marginal value of any unit of output is
given by the height of the de
Bare-bones Calculus Review
Let y = f (x) be a function. The derivative of f at a point x is dened as
lim
x0
f (x + x) f (x)
.
x
If we dene y = f (x + x) f (x), we can write this more succinctly as
y
.
x0 x
lim
We denote the derivative by f (x), or by
poin
Using Budget Lines: A Price Increase with a Cost of Living Adjustment
Y = Spending
on Other Goods
The price of coffee is $4 per cup, you have $100 of
income per week, and you choose 10 cups of
coffee each week, leaving $60 to spend on other
goods each wee