What is the optimal choice of pizza and other goods

Reference no: EM132196843

Question: Suppose two friends are going out to lunch to eat pizza and have the following identical utilities over pizza (P) and other goods (M):

U Toby(M, P) = U Josh(M, P) = M + âˆš P .

Both pizza and other goods have a price of $1. Josh and Toby each have an income of I. Pizza faces a tax-rate of Ï„ so that the after-tax price is (1 + Ï„ ).

1. What is the optimal choice of pizza and other goods for Toby and Josh if they are paying for pizza separately?

2. Suppose that Toby and Josh get their taxes refunded after the meal so that their total income is I + R/2, where R = Ï„ (P Josh + P Toby) is the tax collection. Toby and Josh don't take into account the effect of their choices of M and P on the refund so that their marginal choices don^'t change from question(1). Using their indirect utility function and the formula for R, find the tax rate that maximizes utility for Josh and Toby and explain the economic intuition.

3. Suppose now that Josh and Toby will split the check for their meal. How much pizza will Josh and Toby eat if they are splitting the check? Is it more or less than before?

4. If Ï„ = 0, are their choices socially optimal when they split the check? Derive a mathematical condition that shows whether their choices are optimal or not.

5. Find the tax rate that maximizes utility for Josh and Toby when they split the check and explain the economic intuition.

Reference no: EM132196843

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