Hey could you please answer all the parts of this question ? Question 1: Horizon
ID: 1126900 • Letter: H
Question
Hey could you please answer all the parts of this question ?
Question 1: Horizontal merger analysis There is an oligopoly comprised of three initially-symmetric firms. Demand for firm f's product is qf (p)--pf + (pj + pk), where j and k refer to the other two firms and p = {PnPnPs). Firms simultaneously set prices in equilibrium. Marginal cost is c = 1, If firms 1 and 2 merge, they still produce the same two products, but they maximize joint profits and have new marginal cost cm S c You work for the FTC and are analyzing whether the merger will increase or decrease consumer surplus From econometric analysis, you know that 2, = 2, and = 1. A) Briefly describe the two key forces that determine whether prices increase or decrease. This is the Williamson (1968) merger tradeoff What are equilibrium prices if there is no merger? What are equilibrium prices if firms 1 and 2 merge, as a function of cm? The merging firms argue that the merger will allow marginal cost reductions, and that these reductions will be substantial enough that consumers will be better off with the merger compared to without. Is that plausible? B) C) D) E) (Extra extra credit) Roy's identity states that Marshallian demand (the qr (p) from above) can be written as av qf(p) =-- av' where Y = income and V = indirect utility. Show that Roy's identity holds when qf(p) is as above and indirect utility is F) (Extra extra credit) This form of indirect utility is "quasilinear," which means that indirect utility is measured in units of dollars. Thus, the V from above is conveniently an equation for consumer surplus for a representative consumer! Imagine a worst-case scenario where the merger does not result in any marginal cost reduction. How much would the merger reduce consumer surplus for the representative consumer?Explanation / Answer
( A) Given the three firm scenario where two collude into one firm, the price of the goods produced by the resulting new firm rises giving it a monopoly power. The two key variables to be studied here are the comsumer surplus and the producer surplus. While the consumer surplus falls, on the other hand the producer surplus rises.
(B) When there is no merger-
qf(p)=alpha-beta pf+ gamma (pj+pk); Substituting values of alpha, beta and gamma in the demand function we get,
qf(p)= 2-2pf+(pj+pk)
Equilibrium price vector [p1*,p2*.p3*] is obtained when MR=MC
TRf=pf. qf(p)= 2pf-2pf^2+pjpf+pkpf
MR=dTRf/dqf=2 dpf/dqf-4pf dpf/dqf+pj dpf/dqf+pk dpf/dqf; MR=MC so we get MR=1.
Similarly we get the equilibrium conditions for the other two firms as well.
(C) When there is a merger we simply get MR= cm.
(D) Consumer is not better off as consumer surplus falls post merger.