Question

Problem I-C: Consider the following situation. There are M sellers of used cellphones on the market and many potential buyers who compete in Bertrand fashion to buy these cellphones. Assume cellphones can either be of good quality or bad quality. The reservation seller prices are $150 for a good quality phone, and $20 for a bad quality phone. Buyers are willing to pay up to $200 for a good quality phone, and up to $50 for a bad quality phone. The ratio of good phones to bad phones among these M sellers is 1/2. That means that for every good phone there are two bad phones or that the probability of dealing with a good phone is 1/3 and the probability of dealing with a bad phone is 2/3.

c) What should be the seller’s reservation price for the high quality phone (instead of $150) such that we will not observe an adverse selection problem? Answer: (? 100)

Please answer this question in complete detail as I don't understand this subject too well. Thank you

Answer 1

Consider the given problem here the buyers want to pay “200” and seller wants to receive “150” for a good cell phone and the buyers want to pay “50” and seller wants to receive “20” for a bad cell phone. So, if there are perfect information between buyer and seller, => the all the cell phones will be sold and the price will be within the buyers willing ness to pay and the seller reservation price.

Now, if there is not perfect information regarding cell phone, => buyer will not be able to distinguishe between “good” and “bad” quality of cell phones, => buyer will reduce their willingness to pay. Since there is “1/3” probability of getting “good” cell phone and “2/3” probability of getting “bad phone”, => the buyer will pay the expected willingness to pay.

=> 200/3 + 50*2/3 = 300/3 = 100, => the expected willingness to pay is “100”. So, the buyer will reduce their willingness to pay to “100” for all quality of cell phones. So, if the seller of good quality of phones reduce their reservation price to “100” form “150”, => deal will be possible in the asymmetric information case also, otherwise only bad quality of phones will be sold and all the good phones will go out of market.