Econ 11  Additional Problems
1. Toyota’s technology for producing cars is given by the production function
F
(
K,L
)=
min
{
K, L
}
,whe
re
K
denotes the amount of capital inputs, and
L
denotes the amount of
labor inputs necessary for producing cars.
(
i
)
For a given rental rate of capital
v
and a wage rate
w
,
f
nd Toyota’s input demands
of
K
and
L
necessary to produce a quantity
Q
of cars. Also,
f
nd Toyota’s cost function.
(
ii
)
Suppose Toyota takes the price of its cars as given. If
w
=10
and
v
=10
,
f
nd
Toyota’s longrun supply function of cars (as a function of its price
P
) in the longrun, when
Toyota can adjust both
K
and
L
.
(
iii
)
The demand for Toyota cars is given by
Q
=200
−
5
P
. A
twhatpr
icewou
ldthe
market clear in the long run, if Toyota took the market price as given? In general, how
would the marketclearing price depend on Toyota’s input prices?
(
iv
)
E
f
ectively, Toyota is the only supplier of Toyota cars, and therefore will price its
cars as a monopolist, taking into account the e
f
ecto
fthepr
iceondemand
.Whatquant
ity
will Toyota choose to produce in the long run?
(
v
)
In the short run,
K
is
f
xed at
40
, and input prices are
f
xat
w
=10
and
v
=10
.A
sa
function of
P
, what is the shortrun optimal supply of cars, as a well as the marketclearing
price for Toyotas?
2. Volkswagen has two plants in which it produces its cars: It can either produce cars
in Germany, in a highproductivity, capitalintensive plant, or in Mexico in a lower pro
ductivity, laborintensive plant. The production function for cars in the German plant is
Q
=2
K
2
/
3
L
1
/
3
, while the production function for cars in the Mexican plant is
Q
=
K
1
/
3
L
2
/
3
.
(
i
)
I
fthewagerateinGermany(Mex
ico)is
w
G
(
w
M
), and the rental rate of capital is
v
(the same in both countries), what is the cost function for cars in Germany (Mexico)?
(
ii
)
In the long run, how will the production of cars depend on the price of cars,
P
,the
rental rate of capital
v
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 cunningham
 Economics, Supply And Demand, wage rate, rental rate

Click to edit the document details