Question

Suppose a monopoly produces products that exhibit negative externalities. The marginal private benefit associated with a monopoly’s consumption is MPB = 360-4Q and the marginal revenue associated with its production is MR = 360-8Q The marginal private cost associated with its production is MPC = 6Q The marginal external cost associated with its production is MEC = 2Q Please draw all the above in one graph and answer the following questions:

1). Find the social optimum (Q* and P*)

2). Without any government intervention, the monopoly will product at which point in your graph? Compute the associated price and quantities (Q1 and P1) 

3). Is it necessary for the government to intervene to correct the negative externalities? Why or why not? If the government decides to impose a tax T per unit sold, compute the tax T to achieve the social optimum.

4). Compute the area of net gains.

Answer 1

SOLUTION:-

(Question:1)

MPB = 360 - 4Q

MR = 360 - 8Q

MPC = 6Q

MEC = 2Q

MSC = MPC + MEC = 6Q + 2Q = 8Q

1. Social optimum

MSC = MR

8Q = 360 - 8Q

Q* = 360/16 = 22.5

P* = 360 - 4*22.5 = $270

2. Without intervention, Monopoly produces at MPC = MR

360 - 8Q = 6Q

Q1 = 360/14 = 25.7

P1 = 360 - 4*25.7 = $257.2

3. Yes it is necesaary for the government to intervenue to correct negative externality because private market fails to acknowledge the external cost. Also the equilibrium Quantity reduces at social optimal level which reduces the  profit, so monopolist are not wiling to do that.

Tax = MEC at social Equilibrium level

Tax = 2Q = 2*22.5=$45

4. Total surplus = 0.5(360)*30 = $5400