Question

Graph the production functions below. Q= 6L−1/4L² , L ≥ 8

Q= 1/4L² + 2L, 0 <  L < 8

a. Graph the marginal product and average product curves.

b. Find the maximum attainable production. How much labor is used at that level?

c. Identify the ranges over which the marginal product is increasing and decreasing.

d. Identify the range over which the marginal product of labor is negative. e. Identify the ranges over which the average product of labor is increasing and decreasing.

Answer 1

The production functions are as follows:

  

  

(a) The marginal product of labour and the average product of labour for the first production function is

The marginal product of labour and average product of labour for the second production function is

(b) Taking the first production function

labour	output
8	32
9	33.75
10	35

Putting the values above 8 in the first production function we get the values of output

For L = 8

For L = 9

For L = 10

The maximum attainable production is for Labour inputs above 8.

For, second production function we have

Labour	Output
o	0
1	2.25
2	5
3	8.25
4	12
5	16.25
6	21
7	26.25
8	32

So, we can see that the maximum attainable production is when 8 units of Labour is used.

(c) For the first production function

The marginal product of labour is

Labour	Marginal product of labour
8	2
9	1.5
10	1
11	0.5
12	0
13	-0.5

For L   12, The marginal product of labour will be increasing,

For L 12, The marginal product of labour will be decreasing.

For the second production function, we have the marginal cost.

Labour	Marginal product of labour
0	0
1	2.5
2	3
3	3.5
4	4
5	4.5
6	5
7	5.5
8	6

Hence we can say that for L 0, the Marginal product of labour is increasing

for L 8, the Marginal product of labour is decreasing

(d) The marginal product of labour is

Labour	Marginal product of labour
8	2
9	1.5
10	1
11	0.5
12	0
13	-0.5

From the above table we can see that for Labour less than 12, The marginal product of labour will be diminishing.

We have the marginal product of labour for second production function,

From the table above we can see, as L increases from zero to 8, the marginal product of labour keeps on increasing.

So, for this production function, the marginal product of labour will not be negative in the given range 0 L 8.

(e) The average production of labour is

Labour	Average product of labour
8	4
9	3.75
10	3.5
11	3.25
12	3
13	2.75
14	2.5
15	2.25
16	2
17	1.75
18	1.5
19	1.25
20	1
21	0.75
22	0.5
23	0.25
24	0
25	-0.75

For L   24, the Average product of labour will increase

For L 24. the average product of labour will decrease.

We have the average product of labor of the second production function.

Labour	Average product of labour
0	0
1	2.25
2	2.5
3	2.75
4	3
5	3.25
6	3.5
7	3.75
8	4

Hence we can say that for L 0, the Average product of labour is increasing

for L 8, the average product of labour is decreasing.