Question

A profit-maximizing competitive firm uses just one input, x. its production function is q = 4x1/2. the price of output is $28 and the factor price is $7. the amount of the factor that the firm demands is

Answer 1

Production function is q = 4x^{2} [/tex]

`(dq)/(dx) = (4)/(2) x^{ (-1)/(2) }`

`(dq)/(dx) = (2)/( √(x) )`
π = Poutput. f(x) - x. Pₓ4
`√(x)` - 7x
The amount of the factor that the firm demand is
Poutput*
`(dq)/(dx)` - factor price = 0
28
`(2)/( √(x) )` - 7 = 0

`(56)/( √(x) )` = 7

`(56)/(7) = √(x)`

`√(x) = 8`
The amount of the factor that the firm demand is x = 64 Answer