Question

1. Suppose demand for a product is given by P = 100 - .25 Q and the Supply curve is P = 8 + 0.25Q. What is the market equilibrium values for P and Q ?

2. Now suppose the production of this good generates pollution and the Marginal Social Cost curve (where we add the external cost to the supply curve) is: MSC = 10 + 0.35Q. What are the efficient outcome levels for P and Q?

Answer 1

1. The demand and supply for the product are given as,

Demand: P = 100 - 0.25.Q

Supply: P = 8 + 0.25.Q

At equilibrum, the Supply is equal to Demand. Hence, at equilibrum,

100 - 0.25.Q = 8 + 0.25.Q

or, 0.5.Q = 92

or, Q* = 184

Putting Q* in Supply or Demand function, we get

P* = 100 - 0.25.Q* = 100 - 0.25×184

or, P* = 54

Market equilibrum values of P and Q are P*=54 and Q*=184.

2. the production of this good generates pollution and the Marginal Social Cost curve (where we add the external cost to the supply curve) is,

MSC = 10 + 0.35.Q

Now, the efficient outcome is where MSC and Demand are equal.

Hence, at equilibrum,

100 - 0.25.Q = 10 + 0.35.Q

or, 0.6.Q = 90

or, Q** = 150

Putting Q** in the demand function, we get

P** = 100 - 0.25.Q** = 100 - 0.25×150

or, P** = 62.5

The efficient outcome levels for P and Q are P**=62.5 and Q**=150.

Hope the solutions are clear to you my friend.