Question

Suppose that a company's production for *Q* units of its product is given by the Cobb-Douglas production function shown below, where *K* is dollars of capital investment and *L* is labor hours.

Q = 30K^{1/4}L^{3/4}

(a) Find *Q* if *K* = $625 and *L* = 625 hours.

*Q* =

(b) Show that if*both K* and *L* are doubled, then the output is doubled.

*Q*(2*K*, 2*L*) =
(c) If a capital investment is held at $10,000, graph *Q* as a function of *L*.

(b) Show that if

Step 1

Company's produciton function is given below

Q= units produced

K= dollars of capital investment

L= Labor hours

Given K = $625 and L = 625 hours. By substituting these values we get Q = 18750 units.

Step 2

To show if K and L are doubled then output is doubled.

Let us substitute K = 2K and L = 2L in the produciton funciton as shown below, then we get the total ...

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