1. suppose you work as research economist at the EPA. There are two firms that o
ID: 1168094 • Letter: 1
Question
1. suppose you work as research economist at the EPA. There are two firms that operate in a perfertly competitive marker. This implies that each has the same marginal benefit curve, which in this case is horizontal at MB= $100. Each of the firms, however, has a different marginal private cost schedule
MPC1=20+Q and MPC2=30+2Q
Each firm's production process creates externalities that are valued by society at $10 per unit output
a) show that without governemnt intervention, the firms' profit maximizing outputs are Q=80 for fimr 1 and Q=35 for firm 2, and the amrket is $100
b) Now calculate that socially optimal level of output for each firm
c) your boss knows that the firms are currently producing too much output an simply decides that all firms should cut their output by 15%. Show that this is an inefficient solution to this externality problem
2. Suppose a new submarine for the Navy costs $10 billlion. Half the population (130 million peple) are willing to pay $100 each to have it, and the other half are willing to pay $30 each not to have it. Should it be built?
Explanation / Answer
(1)
(a) Without intervention:
Firm 1 will equate its MB with MPC:
100 = 20 + Q
Q = 80
Firm 2 will equate its MB with MPC:
100 = 30 + 2Q
2Q = 70
Q = 35
In each case, price = MB = $100
(b) Cost of externality will increase the MPC of each firm by $10. This externality-adjusted cost is called Marginal Social Cost (MSC).
Socially optimal output is where the firms equate their MB with MSC (and not with MPC).
Firm 1: MSC = 10 + (20 + Q) = 30 + Q
Firm 2: MSC = 10 + (30 + 2Q) = 40 + 2Q
Firm 1 equilibrium:
100 = 30 + Q
Q = 70
Firm 2 equilibrium:
100 = 40 + 2Q
2Q = 60
Q = 30
(c) This means, quantity derived in part (a) will reduce by 15% for both firms.
Firm 1's new quantity = 80 x 0.85 = 68
Firm 2's new quantity = 35 x 0.85 = 29.75
Both levels of output are lower than socially optimal levels of output. Hence this solution will be inefficient.
(2)
Here, we need to compute the total expected revenue.
Expected revenue = (1/2) x 130 mill x $100 + (1/2) x 130 mill x ( - $30) [ Since people pay NOT to have the submarine, we consider price as negative]
= 65 mill x $(100 - 30)
= $4,550 mill = $4.55 billion
Since the cost is $10 bill > Expected revenue of $4.55 billion, the submarine should not be built, assuming the stated assumptions & probabilities are correct.
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