Answer to Question #121229 in Microeconomics for TOM

Question

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

Tons of fertilizer /
month No of roses/ month Tons of fertilizer /month No of roses/ month
0 0 5 2500
1 500 6 2600
2 100 7 2500
3 1700 8 2000
4 2200
(Hint, write out the average and marginal product for each ton of fertilizer)

What is the efficient level of output it must produce at?

Answer 1

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

APf = Q/F = 2200/4 = 550

b. What is the marginal product of the sixth ton of fertilizer?

MPf = Δ Q/ ΔF = (2600-2500)/ (6-5)

= 100

c. Does this total product function exhibit diminishing marginal returns? If so, 

over what quantities of fertilizer do they occur?

Diminishing marginal returns set in when MPF for some unit is lower than MPF

for the previous unit. This occurs for

F > 3 .

d. Does this total product function exhibit diminishing total returns? If so, over 

what quantities of fertilizer do they occur?

Diminishing total returns set in at the point where total output begins to fall. This 

occurs for F > 6 .