Question

In 1923 during Prohibition, the market for 60 day fermented grape juice was legal, even though it often had up to 12% alcohol content. For buyers, a high quality bottle of juice was worth $6.65, while a low quality one was only worth $3.33. Sellers valued good bottles at $4.99 and bad ones at $1.96. If an uninformed buyer was willing to pay a price of exactly $4.99 for a bottle of juice, then what was the fraction of good ones?

Group of answer choices

0.35

0.50

0.55

0.65

Consider the 1923 market for grape juice one more time, but now assume that uninformed buyers figured 72% of the juice was good and the rest was bad. At the resulting market price, seller surplus from selling good juice is ____ and seller surplus from bad juice is _____.  

Group of answer choices

$0.73; $3.76

$0.73; $2.11

$1.35; $3.76

$1.35; $2.11

Answer 1

a) Let the buyers assume that fraction x of bottles were good and the rest were bad.

Value of good bottles to buyers = 6.65

Value of bad bottles bottles to buyers = 3.33

So Estimated value of all bottles = x * 6.65 + (1-x) * 3.33

so 6.65x + 3.33 - 3.33x = 4.99

or 3.32x = 1.66

or x = 0.5

So the answer is 0.5. i.e. The buyers thought that the fraction of good bottles was 0.5 or 50%

b) If buyers assumed 72% of the bottles were good, then the estimated price to the buyers = 0.72 * 6.65 + 0.28 * 3.33

So Estimated price = 4.788 + 0.9324 = 5.72

Seller's estimate of price of a good bottle = 4.99

So Seller surplus from selling good bottles = 5.72 - 4.99 = 0.73

Seller's estimate of price of a bad bottle = $1.96

So seller surplus from selling bad bottles = $5.72 - $1.96 = $ 3.76

So the correct answer is the first option: $0.73, $3.76

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