Question

Question 5: Sue has 12 tokens for the Huntsville Halloween Faire. Milkshakes cost 8 tokens and tickets to the Haunted House cost 2 tokens. Her value for milkshakes is $2 times the square root of the number of milkshakes. Her value for tickets is $3 - ($1/number of tickets). How many milkshakes and tickets should Sue purchase? A. 4 shakes and 2 tickets B. 4 shakes and 1 ticket C. 4 shakes and 4 tickets D. 9 shakes and 2 tickets E. 1 shake and 2 tickets

Answer 1

Answer 5

The correct answer is (E) 1 shake and 2 tickets.

Utility maximizing condition :

(i) Marginal utility/ Price of all goods must be equal

(ii) It must satisfy budget constraint here P_mM + P_tT = Y, where Pt and Pm are prices of T and M respectively, M and T represents quantity of milkshakes and tickets respectively, Y = Total money she has and here Y = 12

=> 8M + 2T = 12 ------------------Budget constraint

Utility from Tickets is given by : U(T) = 3 - 1/T => Marginal Utility from T = dU/dT = 1/T²

Utility from Milkshakes is given by : U = 2M^0.5 => Marginal Utility from T = dU/dM = 1/M^0.5

Hence (Marginal utility / Price) of milkshakes = (1/M^0.5)/8 , (Marginal utility / Price) of Tickets = (1/T²)/2

From (i) we have Marginal utility/ Price of all goods must be equal

=> (1/M^0.5)/8 = (1/T²)/2

=> T²/M^0.5 = 8/2 = 4

=> M = T⁴/16

Putting this in Budget constraint we get :

8(T⁴/16) + 2T = 12

=> T⁴ + 4T = 24

=> T⁴ + 4T - 24 = 0

Solving this we get T = 2

Hence M = T⁴/16 = 2⁴/16 = 16/16 = 1.

Thus, her optimal consumption is 1 shake and 2 tickets.

Hence, the correct answer is (E) 1 shake and 2 tickets.