Question

3. Consider the monopoly's warranty problem under symmetric information analyzed in the lecture. The value of a product whose value to the consumer is V if the product is operative, and is 0 if the product is defective, where V > 0. The probability for a product to be functional is p, where 0 < p 1. But here let's assume that for some reason the monopoly cannot guarantee more than one product replacement in case the product purchased is found detective. That is, if the product is found detective, the monopolist can provide a warranty to replace the product with a new product; however, if the replacement product fails, then the monopoly cannot replace the replacement product. a. What is the monopoly's expected cost if it provides this type of warranty? b. What is the maximum price the monopoly can charge for the product sold with this type of warranty? c. Wil a monopoly sell the product with a warranty?

Answer 1

Let c be th cost to produe 1 3. umit af output Monopolist is facaal uith (a two situation I. He sells the prodluct and it turns out to be groct 92 this haue to gine case he doesn't uarranty Apradluict and IIHe dells the it tums eut to be dleechu 9n this situation the menopol'stuil hau to frovide the censumer uua produut at geno hat a nu friu Jhis the monopolst u t imurr aLost eauivalent te tuo units by selling Just means unit Camlin

Hemu Erpected Lost 4 menapaist be uill prcbl)x Cost incurerad in prob (n)x cost inuwoud in II 1-)x Cctc Prc X fct CI-Sx 2C 2SC + 2c 1 つ5-つで C(2-) = ( Menopolist cam thag e marimum expected value f censumeu Naus, consume u faced uith tharee Situahons, Camlin

A Finst precluct turni out to be dlefechiue ment product Cwarranty also tusns out ho be dlefechiue Probahiutyf this euent anel the PLA)(1-S) x (1-e) 2-)2 Consuman ecieues vaue eaual to zero VA First product turns out to be dlafecthiue the consu his uuarranty and the ment praduit iGrood Probabiuty a thu euent andl they umu claims PLBI(-S)P Camlin

onsumers valuation in this Case is VB First product hurns to be Gsod ancl the Lensumen eloesn't mead to claim uaranty Probahily thi enent is out C. Consume teueues Nalue eaual to, Ve Henu tonsumers exaected valus PlA) VA tP(B). Vgt PCe). Ve PLA). O (1-S) V + SV 2sv-2v SV (2-5) Camlin

Jhus monopoust can charge maximumm prce eauel to, Prmax ev2-9) if the manopolist delly Nour theproduct ithout waranty then itcan charg marimut frie eaual to the expected Nalue of censumes ithout warranty . expeuted value uarnanty in case QUU is Prob Product is Greod) X V + Prob(Produck is defechine) i's + (1-8) x 6 SV

ten e, uith aut warranty the menopoust can charge a marimuum pnce NW SV In case af No warnanty menapoustu mot obliged to replau the Lemmodlity, Aene it won't care huether dh emmodity u Good or ana ui imply Cary o1 its pradurhidn this to produu eaual to 2.1 Baa Henc sn monopou'st cost unit i cale let, profit un case wlaroranty per af No unit NW rapit in caue per unit waraanty et

ZNW Pv-c 1 p-Expected Cost n case f waranty Sv(2-) 2-)vC) C (2-8) Sinca

(2-8)< 2 fv-c)<(2-ev-C)2(v-C Since protit in caue g warranty is areater thar undn that the monopolist uil sell the preduct uth Warranty profit no waoanty means