Question

In the​ short-run, we assume that capital is a fixed input and labor is a variable​ input, so the firm can increase output only by increasing the amount of labor it uses. In the​ short-run, the​ firm's production function is

q = f(L, K)​,

where q is​ output, L is​ workers, and

K

is the fixed number of units of capital.

A specific equation for the production function is given​ by:

q = 8LK + 5L2 − 13L3

or​ , when

K

​=

22​,

q = (8L×22) + 5L2 − 13L3.

Use this equation to generate the values for output and fill in the table to the right.  ​(Round your answers to the nearest

integer.​)

Production
Labor​ (L)	Output​ (q)
0	0
2	369
4	763
6	nothing
8	1,557
10	nothing
12	2,256

Answer 1

The completed table is given below. The figures have been rounded off to the nearest number. The calculations for each value are given after the table:

L	Q
0	0
2	369
4	763
6	1164
8	1557
10	1927
12	2256

The output calculated by using the given production function with K=22.

q = (8L×22) + 5*(L)^(2) − 1/3*(L)^(3).

For L=0

q = (80*22) + 5*(0)^(2) − 1/3*(0)^(3) =0

For L=2

q = (8*2×22) + 5*(2)^(2) − 1/3*(2)^(3)= 369.3

For L=4

q = (8*4×22) + 5*(4)^(2) − 1/3*(4)^(3) = 762.7

For L=6

q = (8*6×22) + 5*(6)^(2) − 1/3*(6)^(3) = 1164

For L=8

q = (8*8*22) + 5*(8)^(2) − 1/3*(8)^(3) = 1557.3

For L=10

q = (8*10*22) + 5*(10)^(2) − 1/3*(10)^(3) = 1926.7

For L=12

q = (8*12*22) + 5*(12)^(2) − 1/3*(12)^(3) = 2256