Answer
a) 7 dollars for an adult ticket and 4 dollars for a child's ticket, 900 dollars profit
b) 7 dollars for a ticket, 300 tickets sold, 100 dollars profit
c) Children are made worse off, the producer is made worse off, and nobody gains.
d) Part (a) wouldn't change, while parts (b) and (c) would change.
Work Step by Step
a) The maximum adult revenue is 2,100 dollars (7 dollars per ticket * 300 adults). The maximum children's revenue is 800 dollars (4 dollars per ticket * 200 children). The total revenue is 2,900 dollars, and with costs of 2,000 dollars, the profit is 900 dollars. (Please see the tables.)
b) Please see the third table. Profit is maximized at a price of 7 dollars per ticket (300 adult tickets and 0 children tickets are sold).
c) No children were willing to pay 7 dollars for a ticket, so they are made worse off. The producer is made worse off for having a lower profit.
d) The profit from part (a) was 900 dollars, so the profit would decrease to 400 dollars. For part (b), since the profit was originally 100 dollars (and this was maximizing profits), the producer would shut down the show. In that case, everyone is made worse off.
