Consider the following equation where a production function that relates the amo
ID: 1211514 • Letter: C
Question
Consider the following equation where a production function that relates the amount of production per acre to fertilizer use has been estimated: Q^= 1.2 + 8Nit + 5Phos -1.8Nit^2 -0.75Phos^2 -0.5Nit times Phos SE (.01) (1.21) (1.41) (0.51) (.23) (.20) Q = = amount of production in Kilo per acre Nit = amount of Nitrogen fertilizer in 100 Kilos Phos = amount of Phosphorous fertilizer in 100 Kilos N = 30 is the number of observations Find equations describing the marginal effect of nitrogen on production and marginal effect of phosphorous on the amount of production. What do these equations tell you? What are the marginal effects of nitrogen and phosphorous when (i) Nit and Phos=l and (ii) Nit=2 and Phos=2? Comment on your findings. Test whether using more phosphorous leads to lower marginal effect of nitrogen fertilizerExplanation / Answer
Q = 1.2+8N+5P-1.8N^2-0.75P^2-0.5NP
a) MPN = Marginal effect of nitrogen on production = dQ/dN = 8 -3.6N - 0.5P
MPP = Marginal effect of phosphorus on production = dQ/dP = 5 -0.5N - 1.5P
These equations tell about the change in production due to per unit change in nitrogen and phosphorus respectively.
b) When N=P=1
MPN = 8-3.6-0.5 = 3.9
MPL = 5-0.5-1.5 = 3
When N=P=2
MPN = 8-3.6*2-0.5*2 = -0.2
MPP = 5-0.5*2-1.5*2 = 1
As MPN & MPP both the coefficients of P & N are negative so increase in either one or both will decrease marginal productivity.
c) Yes because in the marginal equation MPN Phosphorus P is having a negative coefficient i.e. increase in P will decrease MPN