so im really stuck on this problem. i have tried to figure it out myself but keep getting stuck. can you please help me or direct me in the right direction, thanks. im not the best at microeconomics hence why i am stuck

 

There is an incumbent monopolist using dirty technology (Firm 2), but facing potential entry (from Firm 1). The industry is subject to New Source Review. This means that the existing operator is permitted to continue using dirty technology if it wishes, but any new entrant (potentially Firm 1) would be required to use clean technology. There are no variable production costs, but installation of clean technology would have a cost of C = 2. With dirty technology, Firm 2 would emit pollution of e2 = 0.5q2, where q2 is the firm's output. A firm that uses clean technology would not emit any pollution at all. Inverse demand for output is

 

p = 9 − q1 − q2. (1)

 

The steps of the game are:

1.     The government decides whether to impose a low tax rate on pollution (τ = 1) or a high tax rate (τ = 1.5)

2.      Firm 1 observes the tax decision, then decides whether to enter the industry (n = 2) or not (n = 1).

3.     Firm 2 observes the tax decision and the entry decision, then decides whether to update to newer clean technology (y = 0) or not (y = 1).

4.     If Firm 1 did enter the industry, then both firms simultaneously choose output levels q1 ∈ R+ and q2 ∈ R+. If only Firm 2 is operating, then q1 = 0 and Firm 2 chooses q2 ∈ R+.

 

Firm 1 has profits of zero if it does not enter, and of pq1 − C if it does. Because it would not emit any pollution, it would not have to pay anything for the emissions tax. Firm 2 pays taxes τe2, which is zero or τ q20.5, depending on technology. So it has profits of:

 

p − τ0.5y)q2 − (1 − y)C (2)

 

for y ∈ {0, 1}.

 

Now answer the following questions. You don't need to be alarmed if your answers are not round numbers

 

·       A) Consider step 4 with a clean monopoly, n = 1, y = 0. Substitute q1 = 0, y = 0 and the inverse demand curve, (1), into Firm 2's profits, (2). Then take a first-order condition wrt q2. Solve your FOC for q2 to determine how much output a clean monopolist would produce. How high would a clean monopolist's profits be?

 

·       B) Consider step 4 with a dirty monopoly, n = 1, y = 1. Substitute q1 = 0, y = 1 and the inverse demand curve into Firm 2's profits, then take a first-order condition wrt q2. How high would q2 be? How high would a dirty monopolist's profits be? (You need to give separate answers for τ = 1 and τ = 1.5, or else express output and profits as functions of τ .)  

 

·       C) Consider step 3 with a monopoly. Given that Firm 1 has not entered, for which values of τ (if any) would Firm 2 adopt clean technology? 

 

·       D)Consider step 4 with a clean duopoly, n = 2, y = 0. How high will output and profits be for Firm 1? If you wish, you may take a shortcut by imposing symmetry on Firm 1's FOC.

 

·       E) Consider step 4 with a mixed duopoly, n = 2, y = 1. That is, the entrant is clean but the incumbent is dirty. Verify that output of the two firms will be q1 = 3 +τ/6, q2 = 3−τ/3, for τ ∈ {1, 1.5}. What will the payoffs of the two firms be if τ = 1? What will they be if τ = 1.5? 

 

·       F) Consider step 3 with a duopoly, ie. imagine the choice of Firm 2 after it observes that Firm 1 did enter in step 2. For what values of τ (if any) would Firm 2 adopt clean technology?

 

·       G) Are corrective taxes more effective at encouraging Firm 2 to adopt clean technology when this firm is a monopolist or when it is a duopolist? What is the intuition for your result?

 

·       H) Consider step 2 with a low tax on emissions. With τ = 1, would Firm 1 enter the industry? Explain. 

 

·       I) Would it enter if τ = 1.5? Explain. 

 

·       J) Would Firm 2 install clean technology in equilibrium if τ = 1? What about if τ = 1.5? Explain.

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Status NEW Posted 05 Jun 2017 07:06 AM My Price 13.00

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