Question

A firm uses the inputs of fertilizer and labor to produce roses. Suppose that when the quantity of labor is fixed, the relationship between the quantity of fertilizer and the number of roses produced is given by the following table:

Fertilizer 1 2 3 4 5 6 7 8 9 10

Roses 0 5 18 78 108 136 156 143 123 89

a) What is the average product of fertilizer when tons are used?

b) What is the marginal product of the 6 ^ (th) ton of fertil ?

c) Does this total product function exhibit diminishing marginal returns? If so, over what quantities of fer tilizer do they occur?

d) Does this total product function exhibit diminishing total returns? If , over what quantities of fertilizer do they occur?

a) What is the average product of fertilizer when 4 tons are used?

b) What is the marginal product of the 6th ton of fertilizer?

Answer 1

1) AP of fertilizer when 4 tons are used = Quantity of roses / Fertilizer = 78 / 4 = 19.50

2) MP of the sixth ton of fertilizer = Change in quantity of roses / Change in quantity of fertilizer = (136 - 108) / (6 - 5) = 28

3) Diminishing marginal returns set in when the marginal productivity of fertilizer for some unit is lesser than marginal productivity of fertilizer for the previous unit. Diminishing marginal returns starts when F > 4

Fertilizer	Roses	MP
1	0
2	5	5
3	18	13
4	78	60
5	108	30
6	136	28
7	156	20
8	143	-13
9	123	-20
10	89	-34

4) Diminishing total returns set in when the when the total output begins to decline. It occurs for F>7