Question

A tobacco farmer’s marginal productivity of pesticide is 1-(N/200), where N is gallons of pesticide used. If the price of tobacco is $4 per bushel and the price of pesticide is $1.20 per gallon, how many gallons of pesticide should the farmer use?

Answer 1

Answer

According to Profit maximizing condition a producer or firm hires that amount of Input such that Marginal revenue product of that input is equal to the per unit cost of hiring that input.

Thus using above Profit maximizing condition, a farmer will hire that amount of pesticide(N) such that Marginal Revenue Product of pesticides is equal to price of pesticide per gallon.

Marginal Revenue product of an input is the additional revenue earned when a producer hires one additional unit of input.

Mathematically Marginal revenue Product(MRP) = Marginal Productivity*Price of output.

Here Marginal revenue Product(MRP) = Marginal Productivity of pesticides*Price of tobacco(Output) = (1 - N/200)*4

Also, price of pesticide per gallon = 1.20

Hence, According to profit maximizing condition, MRP of pesticides = Price of pesticides

=> (1 - N/200)*4 = 1.2

=> 1 - N/200 = 0.3

=> N/200 = 0.7

=> N = 140

Hence, Amount of pesticide this farmer should use = 140 gallons.