Refer to Example 3. If labor costs $100 per unit and capital costs $200 per unit, express as a function of two variables, C ( x , y ) , the cost of utilizing x units of labor and y units of capital. Example 3 Production in a firm Suppose that, during a certain time period, the number of units of goods produced when x units of labor and y units of capital are used is f ( x , y ) = 60 x 3 / 4 y 1 / 4 . How many units of goods will be produced by 81 units of labor and 16 units of capital? Show that, whenever the amounts of labor and capital being used are doubled, so is the production. (Economists say that the production function has “constant returns to scale”)
Refer to Example 3. If labor costs $100 per unit and capital costs $200 per unit, express as a function of two variables, C ( x , y ) , the cost of utilizing x units of labor and y units of capital. Example 3 Production in a firm Suppose that, during a certain time period, the number of units of goods produced when x units of labor and y units of capital are used is f ( x , y ) = 60 x 3 / 4 y 1 / 4 . How many units of goods will be produced by 81 units of labor and 16 units of capital? Show that, whenever the amounts of labor and capital being used are doubled, so is the production. (Economists say that the production function has “constant returns to scale”)
Solution Summary: The author explains the cost function of two variables: labor cost and capital cost.
Refer to Example 3. If labor costs $100 per unit and capital costs $200 per unit, express as a function of two variables,
C
(
x
,
y
)
,
the cost of utilizing
x
units of labor and
y
units of capital.
Example 3
Production in a firm
Suppose that, during a certain time period, the number of units of goods produced when
x
units of labor and
y
units of capital are used is
f
(
x
,
y
)
=
60
x
3
/
4
y
1
/
4
.
How many units of goods will be produced by
81
units of labor and
16
units of capital?
Show that, whenever the amounts of labor and capital being used are doubled, so is the production. (Economists say that the production function has “constant returns to scale”)
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