Many people buy used smartphones from eBay, Craigslist, and so on. Some of these

Question

Many people buy used smartphones from eBay, Craigslist, and so on. Some of these phones are good quality, but many others are not, and customers often have a difficult time distinguishing between the two types. Good smartphones are valued at $400 and poor ones at $100. The supply of good smartphones is given by QH= 2PH – 300; that of poor smartphones is given by QL= 4PL-100. If consumers believe that 40% of used smartphones are good quality, then the expected price of a used smartphone is ____. At that price, _____ good smartphones and _____ poor ones will be sold, making the actual likelihood of buying a good phone equal to ____. Requirements: show full solutions.

Explanation / Answer

Good smartphones are valued at $400 and poor ones at $100. If consumers believe that 40% of used smartphones are good quality, then the expected price of a used smartphone is 40% x 400 + 60% x 100 = $220

The supply of good smartphones is given by QH= 2PH – 300; that of poor smartphones is given by QL= 4PL-100. At that price, 2*220 - 300 = 140 good smartphones and 4*220 - 100 = 780 poor ones will be sold, making the actual likelihood of buying a good phone equal to 140*100/(780 + 140) = 15.22%.

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