Question

Suppose that 90 percent of the firms selling good X charge the low price. If the remaining 10 percent of firms charge $50 per unit and the expected benefit of an additional search is $10, then the lowest price in the market for good X is:

please give me detail reasons

A.

$45.

B.

$38.89.

C.

$10.

D.

$0.

Answer 1

We are given that 90% of the firms are selling good X at low price and 10% sell it at $50. This implies that $50 is more than the lowest price.

Also we know that the additional search has expected benefit of $10.

So the probability that the firm is selling at Price Y which is less than 50 is 90% or 0.9 .Benefit is the difference between price $50 and the low price Y

So benefit is 50-Y

And there is 10% probability that the firm is selling at $50 which is not a low price so the there is no benefit . Hence benefit is $0.

Now we have the expected benefit given

So putting the formula

P_A*A+P_B*B= Expected benefit

Expected benefit= 0.9(50-Y)+0.1(0) =10

0.9*50-0.9Y+0=10

45-10 =0.9Y

35 =0.9Y

35*10/9 = Y

So Y=$ 38.89 ie option B

The lowest price for good X is $38.89

(You can comment for doubts)