Question

Suppose a market for financial assets has type Aa and type Bb. Buyers value Aa at $14,500 and type Bb at $11,500, while sellers value Aa at $12,700 and Bb at $10,100. If the buyers cannot observe type, what is the min fraction of type As needed in the market to avoid adverse selection?

Answer 1

It is given that buyers cant observe, which means they do not which financial asset is actually Aa or Bb, while the sellers know it. Now a seller will sell his/her asset as long as the value they are getting is higher than its actual value. So a seller of Aa will sell only when the value he/she is getting is >=12700. A seller of Bb will sell as long as the value is >=10100.

Adverse selection happens when the bad assets, in our case Bb, drive out the good assets. Since the overall price that the market is giving is lower than the prices seller of good assets are expecting, they leave the market, leaving it completely to sellers of bad assets.

Remember that the seller of Aa assets value them at 12700, and will not sell them below this price. We need to keep them to avoid adverse selection. So that's the minimum price that the buyer must pay. But the buyer will not pay 12700 if that's below their expected utility overall. Expected utility of buyers, given x% of assets are Aa, is

14500*x+(1-x)*11500. This is because the buyers value Aa at 14500 and Bb at 11500.

This must be equal to 12700 for sellers of Aa to stay in the market and avoid adverse selection. Hence

14500*x+(1-x)*11500=12700

This gives us x=.4. Which means at least 40% of the fraction of Aa assets should be there to avoid adverse selection.