Question #1 An person obtains utility, U, from units of food, F, and units of dr

Question

Question #1 An person obtains utility, U, from units of food, F, and units of drink, D according to the function. The person has M dollars to spend. The prices per unit for food and drink Pe and Por respectively The person has the opportunity to purchase lottery tickets. The lottery prize is F units of food. Let T represent the number of lottery tickets the person purchases at a price of Pr each. Let T be the total number of tickets sold, excluding tickets sold to this person. Each ticket has the same probability of winning. 1. Write the person's expected utility function. 2. Write the person's budget constraint.

Explanation / Answer

Let the probability of winning be p. Spending on tickets is TPT and the utility derived from tickets is expected utiity

E(U) = p x F' + (1 - p) x 0

a) Then the expected utility function overall = p x ((F + F')D)^0.5 (1 - p)(FD)^0.5

b) Budget constraint is M = DPD + FPF + TPT

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