Chapter 16
NAME
Equilibrium
Introduction.
Supply and demand problems are bread and butter for
economists. In the problems below, you will typically want to solve for
equilibrium prices and quantities by writing an equation that sets supply
equal to demand. Where the price received by suppliers is the same as the
price paid by demanders, one writes supply and demand as functions of
the same price variable,
p
, and solves for the price that equalizes supply
and demand. But if, as happens with taxes and subsidies, suppliers face
diFerent prices from demanders, it is a good idea to denote these two
prices by separate variables,
p
s
and
p
d
. Then one can solve for equilibrium
by solving a system of two equations in the two unknowns
p
s
and
p
d
.The
two equations are the equation that sets supply equal to demand and
the equation that relates the price paid by demanders to the net price
received by suppliers.
Example:
The demand function for commodity
x
is
q
=1
,
000
−
10
p
d
,
where
p
d
is the price paid by consumers. The supply function for
x
is
q
= 100 + 20
p
s
,where
p
s
is the price received by suppliers. ±or each unit
sold, the government collects a tax equal to half of the price paid by con-
sumers. Let us ²nd the equilibrium prices and quantities. In equilibrium,
supply must equal demand, so that 1
,
000
−
10
p
d
= 100 + 20
p
s
.S
incethe
government collects a tax equal to half of the price paid by consumers,
it must be that the sellers only get half of the price paid by consumers,
so it must be that
p
s
=
p
d
/
2. Now we have two equations in the two
unknowns,
p
s
and
p
d
. Substitute the expression
p
d
/
2fo
r
p
s
in the ²rst
equation, and you have 1
,
000
−
10
p
d
= 100 + 10
p
d
. Solve this equation
to ²nd
p
d
= 45. Then
p
s
=22
.
5and
q
= 550.
16.1 (0)
The demand for yak butter is given by 120
−
4
p
d
and the
supply is 2
p
s
−
30, where
p
d
is the price paid by demanders and
p
s
is
the price received by suppliers, measured in dollars per hundred pounds.
Quantities demanded and supplied are measured in hundred-pound units.
(a)
On the axes below, draw the demand curve (with blue ink) and the
supply curve (with red ink) for yak butter.