You are a manager of Mana farm and have been tasked to determine how much maize and wheat can be produced with different types of nitrogen (N). The following are the production functions for maize (M) and wheat (W). M=65.54+1.084NM-0.003N2M and W=68.07+0.830NW-0.002N2W where NM is nitrogen used in maize production in kg and NW is nitrogen used in wheat production in kg. You have 100kg of nitrogen available for 2hactares of land, one for maize and the other for wheat.
The following prices are prevailing in the market; Pm-maize price=K3 per kg, Pw-wheat price=K2 per kg.
a) How much of Nm and Nw can you advise to use?
b) How much M and W will be produced from the levels of nitrogen in (a)?
c) Determine the value marginal products of the two enterprises.
d) What happens to the value marginal products when nitrogen is increased from 100 to 200kg?
e) Is it true that the value marginal product in stage two of production is the demand curve for an input? Explain.