The quality of used books is uniformly distributed between zero to ten: q U[o,10

Question

The quality of used books is uniformly distributed between zero to ten: q U[o,10]. Buyers (q)-q+18 . Booksellers are I. are willing to pay up to 18$ more than the book's quality: willing to sell for at least V () q+15 a. Describe the equilibrium in this market under perfect symmetric information. b. Suppose now that quality is known only by the sellers. Show that there is no equilibrium under which all book are being sold c. Suppose now that buyers are willing to pay iOS per quality-unit: (q)-10-q, and sellers are willing to accept: (q)=q +18. Define equilibrium under symmetric and asymmetric information.

Explanation / Answer

Ans1.

Quality of books is indexed as between numbers ~(0,10)

Since buyers are willing to pay more of $18. So,

Vs=q+18>equal to 10+18

Therefore, q=10

This means 10 buyers willing to pay more than 18$.

Such that equilibrium lies between 0 and 10.

Ans2.

If quality is known only to sellers. Then,

Vs=q+15>10

Vs= - 5

Therefore, due to negative value equilibrium condition does not hold when info wise known to sellers only about quality of the books.

Ans 3.

Now if buyers are willing to pay 10$.

Vs=10q>equal to 10

So, q=1

Such that equilibrium under symmetric information is between 1 and 10

Under asymmetrical information

10q>q+18

9q>18

q>equal to 2

Therefore, q=2

Such that in asymmetric information equilibrium lies between 2 and 10.

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