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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
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 Spring '08
 cunningham

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