Question

A juice shop in Santa Barbara serves two types of consumers: tourists and locals. Tourists’ inverse demand per day is P(q) = (50−q)/5 . Locals’ inverse demand per day is P(q) = (500−q)/ 50 . In order to sell a total of 55 juice bottles per day, what price should the shop charge per bottle? (a) $12 (b) $10 (c) $9 (d) $8 3.

(continued from previous question) Assume that the number of tourists coming to Santa Barbara double. (This means that demand from tourists at every price level doubles.) But, at the same time, due to an economic recession, the local demand becomes more price sensitive. P(q) = (500−q)/ 100 .

Which statement is correct?

(a) To maximize revenue, it is optimal to price high enough to only target tourists.

(b) At the revenue maximizing price, there is higher revenue generated from the local population relative to tourists.

(c) The revenue maximizing price is $4 per bottle.

(d) If the tourists stop coming (demand decreases to 0), to maximize revenue the shop owner would increase the price.

A is correct but why?

Answer 1

given

....................(1)

and .............(2)

.so to sell a total of 55 bottles, the price of juice should be $9

from equation 1 at price $9,

q= 5

in equation 2 at price $ 9, Q =50

so total sold bottle Q= 5+50=55

here, in this case, the number of visitors has been doubled which implies that the demand for the bottles will be also doubled. Whereas the locals are price sensitive, for them the juice bottles are highly elastic, which means they will stop buying a bottle if price increase. If we carefully observe the demand for bottles at $9 , it is maximum for local consumers.T he shopkeeper on the other hand willing to maximize his profit, by increasing the price. so it means it will lose its local consumer's demand so to compensate it, he has to increase the price for the tourists. Tourist are not price sensitive on the other hand, for them the juice bottle is inelastic, they don't have any other similar alternative for it, so they will have to buy it on any cost (increased price). Hence to increase its profit the shopkeeper can opt to price discrimination, by increasing price for tourists, and keeping unchanged for the locals.