In Order to Attract Listeners, a Radio Station Gives Away

question 63

Essay

In order to attract listeners, a radio station gives away money if listeners correctly identify the amount of money found by a "treasure hunter". A contestant would guess the amount on the air, and the disc jockey would then play a tape in which the "treasure hunter" said how much he had found. If the caller guessed correctly, they won the amount of money found by the treasure hunter. If they guessed incorrectly, they received nothing. Suppose that the treasure hunter either found $50 or $100. The payoff matrix represents this game: $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { Treasure Hunter Finds: } \\\begin{array} { l r r c } & & \$ 50 & \$ 100 \\\hline \text { Caller Guesses } & \$ 50 & \$ 50 & \$ 0 \\& \$ 100 & \$ 0 & \$ 100\end{array}$$
If the station plans on running the game every day for 10 days, how much will they pay out?

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Definitions:

Quantity Demanded

The total amount of a good or service that consumers are willing and able to purchase at a given price level.

Inelastic

A description of a situation where the demand or supply for a good or service is relatively unresponsive to changes in price.

Price Elasticity

A measure of how much the quantity demanded or supplied of a good changes in response to a change in its price, indicating the sensitivity of demand or supply to price changes.

Quantity Demanded

The total amount of a good or service that consumers are willing and able to purchase at a given price, holding all other factors constant.