Assignment 3 (Optional) Total Marks: 90 Problem Solving Questions Read each part of the questions very carefully. Show all the steps of your calculations to get full marks. B1.

******* Solving ********* **** **** **** of *** ********* very ********* **** all *** ***** ** your ************ ** *** **** ***** ** *** ************* ****** demand is * * *** **** (a) ** two ***** ******* ** **** market **** constant ******** *** average ***** **** find the Cournot *********** ****** and ****** *** *********** **** * ***** **** ***** ****** choice * * as ***** **** **** ***** problem ** ** ******** its ****** by choosing *** ****** ***** * q ** **** * ******** 1 * ***** *** **** * produces * * ***** **** ***** ******** supplied ** * * qq * ****** 21 qqQ +≡ *** market ***** will be *** 2 * *** *********** 1’s profit ************ ******** *** * ) * * * * * 121211 ** *** * ***** *** +−= π * qFirst ***** *********** * ) * * ****** 121 1 * = −−++−= *** *** qqq * ** **** 1202 02120 2 * ** 21 * * ** ** *** **** ******* =−−⇒ Page * of ** ******* **** ***** best ******** ** * * ** **** 1’s reaction function *** * ) * *** * ** q *** *** ** ******** *** ******* maximization ******* faced by *** two ***** *** ********* ** this **** **** 2’s **** ******** ** 1 * ** **** 2’s ******** ******** **** **** the **** ********** **** ** **** ( ** *** 112qqRq− ** (2)The ******** ** *** ******* also ******* **** ** the ************ *********** both ***** **** produce *** **** level of output: * * 2 * 1 * qq * * *************** * 21 * ** = = **** ****** *** ** *** and solving *** * * ** **** 2 *** ** qq− * 4012031202****=⇒ **** ******* * q qqSo *** Cournot-Nash *********** output *** * ) * * **** * * * 1 * ****** ***** ****** ** the equilibrium: * * * * * * * * * * * * * * * 2 * ** ** *** * ***** *** +−= π * ** * * ***** ******* ************** **** −+−=Because ** *** symmetry of *** ******* **** ***** ****** ** **** as **** ***** ****** ** *** ************ * * * ) **** * 2 * 11 * * * 12 * * * *** ππ ****** * ** 16 ******** **** the monopoly ****** *** ****** ** ***** ** only *** **** **** ******** cost ** =c The ************** ******* is to ******** profit ** ******** its ****** level * *** ******************* ******* of *** ************** ( * * * * QQQm 10 *** *** **** *** ***** order *********** * * ****** = *********** *** *** ** Q * π 60 **** ***** **** =⇒ ******* * * QSo *** ***************** *********** output ** *** ********** *** 60* =mQThe profit-maximizing equilibrium price of *** ********** *** 7060130130 ** = ******** mm ** *********** ****** ** the monopolist *** ************** *** * ******** *** QcP ** *** ***** *** information **** parts *** *** (b) ********* * * *** payoff ****** ***** *** ********** available ** **** ** *** ******* *** ** ******* *** ******* *********** quantity ** half *** monopoly ************ **** firms ****** the ******* *********** ******** **** ***** *** ******* equilibrium ****** ***** ** ********** in **** *** ********* ********* **** the monopoly ****** ******* **** **** **** *** ******** ******* ( * 18003600 2 * * * * ** * === * ππ ** **** for ******** **** * produces *** Cournot output ** * ** while firm * produces **** the monopoly ****** * * ** 60 * 1 2 * * 2 = ** *** *** ****** ***** ***** ** * ) 603040130 ******* Firm 1 earns * ) **** ********** = ******** *** ** and **** * earns ( * **** )3010(6022 = ******** *** ** **** *** ***** are ******** ** *** ************* 4 of 16 ******** ****** ** ****** ** a game ***** each ** *** *** ***** *** ****** between *** **** the ******** ******** (3) ** the Cournot *********** ******** **** is ** ******** ***** 30 * ** ** * ** **** * ** 1 ** **** **** **** **** 40 * =q **** **** **** ******* **** is the Nash *********** (or *********** ** the **** *** constructed ** **** **** Is ***** *** ***** strategy **** *********** ** this game? ** *** **** is *** ***** strategy **** *********** *** *************** **** ** **** *** ** * typical ************ ******* **** ***** producing the ******* equilibrium ****** ** choosing 40 =q is *** dominant strategy *** **** **** ** **** * ******* ** 1 ** *** best ******** for Firm * ** to ****** ** * =q ******* 18002000 **** If **** 1 chooses ** 2 ** *** best ******** *** **** 2 is to choose 402 ** because 1500 **** **** **** 40 2 ** ** the ******** ******** *** **** 2 ***** the **** ** ********* ** *** argue **** ** 1 ** ** **** *** dominant ******** for **** * This **** *** a ****** **** *********** ***** each **** ***** its ******** ******** **** ** ( * 4040 ** * * ** is *** unique **** *********** of **** **** **** **** **** ** * pure ******** **** ************* this **** there ** ** ***** ******** **** *********** ******* **** **** has * ******** ******** which ** ** produce *** ******* *********** ****** ***** **** firm * ** ******** 40 * =q **** * *** ******* probability *** **** ******** of **** 2 ** ** ****** ** * ** with * 100 ******* probability rather than to ****** * ********** strategy over ** 2 ** *** ** * =q **** versa Page * ** ** ******* *** ************** * ********** ********** **** ******* two ******* **** *** David They **** ** ** divide ******* **** **** ***** ** spend ** most **** **** *********** **** *** ******** *** ***** *** Alan **** **** an ***** ***** either accepts ** ***** **** with * counteroffer the next *** *** ** *** ****** day ***** **** ** **** *** ***** ***** ** **** cannot ***** an agreement in **** **** **** players get ****** ****** **** *** David ****** ** ***** degree ** *********** ******** ******** ****** ** ** *** *** *** David’s ******** ****** is ** per day We **** assume **** ** * player is *********** ******* *** ****** ** **** ****** *** *** **** ** most ********* ** his opponent *** Draw *** ********* **** of **** ********** gameSee Figure ******** **** the ******* ******* *********** ** this bargaining ******* ****** ******** ******* ******* equilibrium ** this ********** **** ***** ****** * **** ****** ( * [ * **** ** ***** −−−=X ** ******* and ( ** * βα ** **** 1 − ******* * to David ***** ******* the ***** In ****** * ***** ****** ( * **** *** −=X to Alan and * * **** 5555 * − ******* X ** himself **** ******* *** ******* period * Alan ******** *** ***** ** himself ***** ** * **** * ** ***** ************ *** ******* ****** * ***** ****** * =X ** Alan and * * * * − * to ******* Alan ******* *** offer[Note: See Chapter ** ******* ****** on ********* bargaining ******* # *** ** **** ** understand how ** derive *** ******* ******* *********** ****** ** ******** ************* **** ** the ***** ******* of **** ********* *** ***** ***** ** ********* at *** *** ** *** ***** *** ** ****** * **** ****** * )[ * **** ** ***** *********** to ******* *** * * * * βα ** **** * *** −=− * ** ***** ***** ******* *** ***** ** *** **** **** ***** the first *** ** **************** 6 ** ** ******** If ***** becomes **** ********* **** **** ****** to the equilibrium payoff to Alan?If ***** ******* **** impatient ** **** ******** *** ****** ****** ** a ****** **** In ***** ***** *** ***** ** ********* ******** ****** β ********* ** he ******* **** ********* **** **** ( * * * **** ** **** ********* ** * ***** ******* ** this **** at the *** ** ***** *** *** ***** ** *** ****** ********* **** * ******** ** ** all other ****** ********* ******** B3 [15 ********* ***** *** ********* ** ** ************* ******** **** * the ****** of *** two firms ** ************* *** ******** strategy ***** could ** ****** **************** ** “passive” *** aggressive ******** involves a large increase ** ******** ***** ** increasing *** ******** ****** share while the passive ******** ******** ** change ** *** ******** capacity **** * *** smaller competitor ** also ********* its ******** ********* strategy; ** will **** ****** ******* ** ********** ******** and * ******* ******** *** table below shows *** ******* associated with **** **** ** choices ***** ********** ******* **** 1 ********** ** * 33 10 ******* 30 ** ** 12(a) ** **** ***** ****** ***** ********** ************** **** is *** **** *********** *** equilibria)? ** there any ***** ******** **** equilibrium ** this game? ** *** **** is the mixed ******** Nash equilibrium (or ************** **** * ******* “aggressive” *** best response *** **** * ** to ****** “passive” Because ** 30 **** If **** * ******* “passive” *** **** ******** *** **** * ** to ****** ************* ******* ** ** **** This ******* that “passive” ** * ******** ******** for **** * ******* there ** ** ******** strategy *** **** 2 ** **** ******** * **** ****** *** dominant strategy ************* Firm * ******* * **** 1 *** * dominant strategy **** **** its best ******** **************** **** ** the **** **** equilibrium in *** ***************** ********* ** no ***** ******** **** equilibrium ******* *** of *** ******* **** * *** * ******** ******** in **** **** ***** that **** * ** ******** ************* **** * *** ******* *********** *** **** response ** **** * ** ** choose “aggressive” with a 100 ******* probability ****** than ** choose * ********** ******** **** ************* *** “aggressive” **** ********* 7 ** ** ******** assume **** **** * can ****** ***** and *** ******** commit ** *** ******** ********* ******** (b) **** the ********* **** ** **** sequential **** **** ** the ******* ******* ************ What is the ***** ******* of **** game?See Figure ***** *** *** ********* **** ************** ** this ****** shown in ****** ***** ** **** 1 *** ****** ***** **** ** ** ******* **************** Firm * will choose “passive” and **** 1 **** receive ** ** Firm * ******* chooses ************* **** **** * **** ****** **************** *** Firm * **** ******* * ****** ** ** ********* ** **** 1 *** **** ***** ** **** best ** select “aggressive” ** ***** **** Firm 2 **** ****** *** best ******** “passive” ******* **** * * ****** of ** *** **** * a ****** ** ** The Subgame perfect equilibrium:In ****** * **** 2 **** choose ************* ** Firm * ******* “aggressive” ** ****** *** period * **** 2 **** choose **************** ** Firm * chooses ************* ** ****** 1In period 1 **** * **** choose “aggressive”The final ******* ** this ******* ****** * **** * **** ****** **************** and ** ****** * **** 1 **** ****** ************* earning **** * * payoff ** 33 *** **** 2 * ****** of 10(c) ** **** * ********* ** **** **************** ** **** * plays **************** **** ** ** ******** ** Firm 1? If this threat ** *** credible ** Firm 1 **** ***** Firm * do ** **** *** ****** *********** firm * threatens ** play “aggressive” ** Firm 1 ***** **************** it **** *** ** ******** ** **** * ******* Firm * ***** **** if ** ***** **************** in period * Firm ***** **** response in ****** * **** ** ************* Because * ** > **** ***** problem ** **** once Firm * has **** *** choice **** * expects **** * ** do *** rational thing Firm * *** **** *** ****** ******** ** ** ***** ****** ****** ** **** would ** ****** off ** it ***** ****** ****** ** play **************** if Firm * ***** **************** *** way for **** * ** **** such * commitment is ** ***** someone **** to **** *** choices *** ******* Firm * ***** **** a lawyer *** ******** *** ** play **************** ** **** * plays **************** ** **** * ** ***** ** these ************ the ********* ** ********* different **** its ***** ** **** ** **** 1 ***** about **** 2’s instructions ** *** lawyer then it ***** **** ** ** ***** **************** ** **** *** up **** * payoff of 25Page * ** 16 PagesSo the ******** ***** *** **** * to do ** ** **** ************* and *** a ********** ****** ****** ** ** See ****** B3(c) *** an ********* **** ************** ** **** ****