Sheena has a budget of $560 which she can allocate to buying tickets for either

Question

Sheena has a budget of $560 which she can allocate to buying tickets for either professional sports games or the ballet. The price of a ballet ticket is $80 and the price of # of a sports ticket is $160. Her total utilities from different quantities of events are given in the table to the right. Use the information in the table to answer parts a through d Events TU for Ballet Tickets TU for Sports Tickets 60 96 126 146 19 a) Calculate the MU per dollar spent for ballet and sports tickets. Complete the table below. # Of Events MU of Ballet Tickets MU/P of Ballet Tickets TU for Sports Tickets MU of Sports Tickets MU/P of Sports Tickets TU for Ballet Tickets 19 60 96 126 146 Type integers or decimals rounded to three decimal places as needed.) b) How many of each ticket will Sheena purchase to maximize her total utility? Sheena will purchaseballet ticket(s) and sports ticket(s) (Type whole numbers.) c) What is her total utility and how much does she spend? Sheena's total utility is.util(s) and she spends a total of $. d) Could she have purchased 4 ballet and 4 sports tickets? Sheena would have to spend Sto buy that bundle of tickets. She has | income to do so, so the answer is

Explanation / Answer

(a) MU = Change in TU / Change in number of events (Q)

(b) Utility is maximized when (MU/P) for Ballet tickets = (MU/P) for Sports tickets

From above table, (MU/P) for Ballet tickets = (MU/P) for Sports tickets = 0.225, when

Number of ballet tickets = 3

Number of sports tickets = 2

(c)

Total utility = 63 (From ballet) + 96 (From Sports) = 159

Total spending = 3 x $80 + 2 x $160 = $240 + $320 = $560

(d)

Sheen would have to spend $960 [= 4 x $80 + 4 x $160 = $320 + $640].

She has less (Insufficient) income to do so, so the answer is NO.

Q TU (Ballet) MU (Ballet) (MU/P) (Ballet) TU (Sports) MU (Sports) (MU/P) (Sports) 1 19 19 0.238 60 60 0.375 2 45 26 0.325 96 36 0.225 3 63 18 0.225 126 30 0.188 4 77 14 0.175 146 20 0.125

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