Additional Exercises

Additional Exercises - Economics 210C Exercises Spring 2011...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Economics 210C Exercises Spring 2011 1. Consider a modification of the Cournot duopoly model, under which producers can revise their supply decision to match their rivals supply if it exceeds their own. More specifically, the firms play a market game that has the following two stages: Stage 1: The firms choose simultaneously what quantity to supply. Stage 2: The firms are informed of each others quantities chosen in stage 1. A firm with a smaller quantity can either keep its quantity or revise it to match the quantity of the other firm. Let p ( Q ) = a- bQ be the inverse demand and C i ( q i ) = cq i the cost function of firm i , i = 1 , 2. Assume a,b,c > 0 and a > c . Can there be a subgame-perfect equilibrium for the above 2-stage game, in which each firm chooses 1/2 of the monopoly quantity? Support your answer. 2. Consider a Cournot oligopoly with three firms. Let p ( Q ) = 150- Q, 0 be the inverse demand and C i ( q i ) = 18 q i + q 2 i the cost function of firm i = 1 , 2 , 3. (a) Show that any two firms would have profit incentives to merge into one. (b) Show that consumers become worse off when two firms merge into one. 3. Two firms, A and B, produce a homogeneous good which they sell in two markets, 1 and 2. Firm i = A,B has cost function C ( q i 1 + q i 2 ) = 1 2 ( q i 1 + q i 2 ) 2 , where q i 1 and q i 2 are the quantities firm i sells in market 1 and market 2, respectively. The inverse demand function is the same in each market and is given by P ( Q k ) = 20- Q k , where Q k = q A k + q B k for k = 1 , 2. (a) Write down firm As profit (from sales in both markets) as a function of q A 1 ,q A 2 ,q B 1 ,q B 2 . Answer: Denote firm As profit at quantities q A 1 ,q A 2 ,q B 1 ,q B 2 by A ( q A 1 ,q A 2 ,q B 1 ,q B 2 ). Note first that firm As total production cost at quantities q A 1 ,q A 2 ,q B 1 ,q B 2 is 1 2 ( q A 1 + q A 2 ) 2 1 and its total revenue is (20- q A 1- q B 1 ) q A 1 + (20- q A 2- q B 2 ) q A 2 . Thus, A ( q A 1 ,q A 2 ,q B 1 ,q B 2 ) = (20- q A 1- q B 1 ) q A 1 +(20- q A 2- q B 2 ) q A 2- 1 2 ( q A 1 + q A 2 ) 2 . Firm Bs profit function can be similarly determined. (b) Consider the case where the firms sell the good in market 1 and market 2 simultaneously. Write down the strategy set for each firm and find the Nash equilibrium. Answer: Note that firms production capacities are not limited. This means that each firm can supply any nonnegative quantity to either market. We conclude that when the firms sell the good in both markets simultaneously, a generic strategy for either firm consists of two nonnegative quantities, with one to be sold in market 1 and the other in market 2. Thus, firm As strategy set is S A = { ( q A 1 ,q A 2 ) | q A 1 ,q A 2 } and firm Bs strategy set is S B = { ( q B 1 ,q B 2 ) | q B 1 ,q B 2 } ....
View Full Document

This note was uploaded on 12/26/2011 for the course ECON 210C taught by Professor Qin during the Fall '09 term at UCSB.

Page1 / 21

Additional Exercises - Economics 210C Exercises Spring 2011...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online