Question

Consider a market where the demand and supply for the good are described by the following equations: begin mathsize 14px style straight Q subscript straight D space equals space 225 space minus space 3 straight P end style and begin mathsize 14px style straight Q subscript straight S space equals space minus space 22.5 space plus space 1.5 straight P end style. If the market is perfectly competitive, the good is rival and excludable, and there are no externalities, the producer surplus is $1,933.00 $1,200.00 $1,800.00 $600.00

Answer 1

Solution:

As per the given information, we have the following equations:

Demand function: Qd = 225 - 3P

Supply function: Qs = -22.5 + 1.5P

Then, with rivalrous and excludable kind of good (that is a private good) with no externalities, equilibrium occurs where the demand curve and supply curve intersect. So,

225 - 3P = -22.5 + 1.5P

225 + 22.5 = 1.5P + 3P

247.5 = 4.5P

P = 247.5/4.5 = $55 per unit

So, equilibrium quantity = 225 - 3*55 = 60 units

We can modify the supply function into inverse supply function: Qs = -22.5 + 1.5P, so writing P in terms of Qs:

P = (Qs + 22.5)/1.5

P = (1/1.5)*Qs + 15

So, price intercept of supply curve (found using Qs = 0) is 15.

Producer surplus = (1/2)*equilibrium quantity*(equilibrium price - max(price intercept of supply curve, 0))

Producer surplus = (1/2)*60*(55 - 15) = 1200

Thus, the correct option is (b) $1,200.00.