Industrial Technology Exercise

Industrial technology exercise.

b) We do the first order condition (FOC) with respect to each and get 3 equations expressing prices for each firm:

The next step with equations (2), (3) and (4) above was done with STATA performing Ordinary least squares (OLS) model to obtain the values of parameters α, β, b, d, 1 , 2 , 3 . These results were calculated:

However, I did not manage to make further calculations and obtain exact values of parameters.

Table from STATA OLS calculations for question 1

If all 3 firms form a horizontal cartel I assume that then they have a joint profit maximization function which would look like:

a) We do the first order condition (FOC) with respect to each and get 3 equations expressing prices for each firm:

Inserting these values mentioned above we obtain the discount factor:

The punishment strategy under Bertrand price competition is the reversion to the Nash equilibrium making all the profits equal to zero for all firms.

3. After the cartel has been formed, the fourth firm (firm h) enters the market with the cost parameter 4 =5.

Assuming that the fourth firm joins the cartel the profit maximization function should be:

When the fourth firm enters the market, assuming that 1 = 2 = 3 = 4 because they form a cartel of n=k (4=4) the equilibrium price decrease a little, since more firms join in and it’s harder to sustain the cartel: ∗ = 51+0.2∗4−0.18(6−3−3−3) 2∗0.2 > ∗ =36.09 and the equilibrium quantity becomes lower as well:

Also, the minimum discount factor becomes higher when the fourth firm joins, since critical discount factor is increasing in n (number of firms).

4. Entering the market is costly (a lump sum). If there was no cartel, then the fourth firm would not enter.

I checked the book “Industrial Organization Markets and Strategies” by Paul Belleflamme and Martin Peitz – both 1st edition via internet and 2nd edition as a print version in the Vilnius University library. I could not find any info regarding this question except for deriving the social optimum and the assumption in the book about the planner that can regulate entry but not output and finance the fixed entry costs by a lump sum tax on the consumer’s income, however, I’m pretty sure that is not the case I was asked here

5. How does the entry compensate the loss of consumer surplus and change the profitability of a cartel.

Clearly the entry lowers the profitability of the cartel and makes it harder to sustain than it was with 3 firms. The entry for the fourth firm in a group pricing increases the dead weight loss and decreases the consumer surplus, however, according to the exercise. However, I would say that the consumer surplus increases, since the equilibrium price decrease. However, it could be that everything in this model is flawed, since I did not manage to estimate the parameters.