Question

Peru Nut Growers Association hires a team of botanists to develop a new “national nut,” which it intends to export globally.

The demand curve for Peru Nuts is given by Qd = 120 − 0.03P, where Q is the quantity in thousand of tons of nuts, and P is the price of a ton of nuts (in US dollars).
The supply curve for Peru Nuts is given by Qs = 0.11P.

Compute the equilibrium price, quantity, and producer surplus for Peruvian nut growers.

Answer 1

Equilibrium price:

Equilibrium price is calculated at a point where quantity demanded = quantity supplied.

Qd = Qs
120 - 0.03P = 0.11P
120 = 0.11P + 0.03P
120 = 0.14P
120 / 0.14 = P
P = $857.14

To calculate equilibrium quantity, put value of P in the demand and supply equation:

Qd = 120 - 0.03 ($857.14) = 94.28
Qs = 0.11 x $857.14 = 94.28

Thus, 94.28 units is the equilibrium quantity, because Qd = Qs at this quantity.

Producer surplus:

Produer surplus = (equilibrium price - minimum price to sell) x equilibrium {Minimum price to sell can be calculated by keeping quantity sold or Qd to be 0 and the corresponding price can be the minimum price}
PS = ( 857.14 - 4000) x 94.28
PS = - 296308.841

Thus, producer surplus is negative in this case.