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Problem set 6.
Due week 8
at the beginning of your tutorial.
Problem 1. Perfect Substitutes Production.
The firm’s technology is such that one unit of output can be produced either using 2 units
of capital or 3 units of labour. Denote with
L
the amount of labor,
K
 the amount of
capital. The wage rate is 2, the rental rate on capital is 3.
a)
Write down the firm’s production function. Is it CRS, DRS or IRS?
b)
What is the optimal way to produce 1 unit of output?
c)
What is this firm’s cost function
C
(
y
)?
Problem 2. Perfect Complements Production.
The firm must use 2 unit of capital with 3 units of labour to produce each unit of output.
Denote with
L
the amount of labor,
K
 the amount of capital. The wage rate is 2, the
rental rate on capital is 3.
a)
Write down the firm’s production function. Is it CRS, DRS or IRS?
b)
What is the optimal way to produce 1 unit of output?
c)
What is this firm’s cost function
C
(
y
)?
Problem 3. CobbDouglas Production with Constant Returns to Scale.
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 Three '09
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