2. The expected value of Illegal parking Aa Aa H Sam has difficulty finding park

Question

2. The expected value of Illegal parking Aa Aa H Sam has difficulty finding parking in his neighborhood and, thus, is considering the gamble of illegally parking on the sidewalk because of the opportunity cost of the time he spends searching for parking. On any given day, Sam knows he may or may not get a ticket, but he also expects that if he were to do it every day, the average amount he would pay for parking tickets should converge to the expected value. If the expected value is positive, then in the long run, it will be optimal for him to park on the sidewalk and occasionally pay the tickets, in exchange for the benefits of not searching for parking. Suppose that Sam knows that the fine for parking this way is $100 and his opportunity cost (oC) of searching for parking is $15 per day. That is, if he parks on the sidewalk and does not get a ticket, he gets a positive payoff worth $15; if he does get a ticket, he ends up with a payoff of . Given that he still does not know the probability of getting caught, compute his expected payoff from parking on the sidewalk when the probability of getting a ticket is 10% and then when the probability is 50%. Probability of Ticket 10% 50% EV of Sidewalk Parking (OC = $15) Based on the values you found in the previous table, use the blue line (circle symbols) on the following graph to plot the expected value of sidewalk parking when the opportunity cost of time is $15. Now, suppose Sam gets a new job that requires him to work longer hours. As a result, the opportunity cost of his time rises, and he now values the time saved from not having to look for parking at $30 per day. Again, compute the expected value of the payoff from parking on the sidewalk, given the two different probabilities of getting a ticket. Probability of Ticket 100% 50% EV of Sidewalk Parking (OC = $30) Use the orange line (square symbols) on the following graph to plot the expected value of sidewalk parking when the opportunity cost of time is $30.

Explanation / Answer

If sam's side park and did not get a ticket he will earn $15 but if he get a ticket he will get = opportunitiy cost of finding a legal parking - ticket charge = $15 - $100 = -$85.

Expected payoff =summation of all (probability for an even to occur*value of event)

Hence when Probability of getting a ticket is 10% or 0.10 then expected payoff = probabilty of getting a ticket*payoff by getting a ticket + probability of not getting a ticket*payoff when does not get a ticket.

= 0.10*(-85) + (1-0.10)(15) = $5.

When probaility of getting a ticket is 50% or 0.5 = 0.50*(-85) + (1-0.50)(15) = -$35.

Thus,

Now in second part of the question, the opportunity cost of finding a legal parking has rised to $30.

Therefore,

Probability of getting a ticket is 10% or 0.10 then expected payoff = probabilty of getting a ticket*payoff by getting a ticket + probability of not getting a ticket*payoff when does not get a ticket.

= 0.10*(-70) + (1-0.10)(30) = $20

When probaility of getting a ticket is 50% or 0.5 = 0.50*(-70) + (1-0.50)(30) = -$20

Thus,

:

Now during 40 days he gets tickets for 9 times, thus probability to get a ticket = number of times Times he gets ticket/total number of days of illegal parking = 9/40 = 0.225 0r 22.5%

Hence chance of receiving ticket is 22.5%.

Given this chance lets calculate total expected value he gets when opportunity cost of finding a legal parking is $15 = 0.225*-85 + (1-0.225)*(15) = -$7.5

hence he will NOT parked illegaly when opportunity cost of finding a parking is $15.

Now lets calculate total expected value he gets when opportunity cost of finding a legal parking is $30 = 0.225*-70 + (1-0.225)*(30) = $7.5

hence he WILL parked illegaly when opportunity cost of finding a parking is $30.

Probability of ticket 10% 50% EV of sidewalk parking $5 -$35

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