The demand function of widgets is given by p 200 q 2 where

The demand function of widgets is given by p = 200 q 2 where p is the unit price in U.S. Dollars and q is the quantity of widgets demanded each week. If the supply function is p = q 2 + 38

Find

(a) the equilibrium price p and the equilibrium quantity q ,

(b) the producers’ surplus

(c) the consumers’ surplus

Solution

The demand function of widgets is given by p = 200 q 2 where p is the unit price in U.S. Dollars and q is the quantity of widgets demanded each week.

If tThe supply function is p = q 2 + 38

a)  Equilibrium quantity is reached when demand=supply. 200 q 2 =q 2 + 38, q2=81 is the Equilibrium quantity

q* = 81. The price at q* is p*. Therefore, p* = 200-81=119

(b) the producers’ surplus

We know the equilibrium is 119, 81 is p*,q*, and supply is p2 = q 2 + 38,so, when q2=0 we have p2=38. and when p2=119 we have q2=81. So, 0,119 is projection of equilibrium point on Y axis. Producer\' surplus = 1/2 * (119-38)(81) = the producers’ surplus: 3280.5

c)the consumers’ surplus:

Demand curce is  p = 200 q 2. considereing when q=0 , p=200. And at equilibrium p,q is 119,81. So Consumer\' surplus is .5*(200-119)(81) =  3280.5