Question 1 - Consumer theory (22 Points) Noel's preferences for donuts (x) and apples (y) can be represented by the utility function U(x, y ) = (27+42) 2 We also know that Noel's indirect utility function is given by: V (Px, Py, I) = (Px + Py) I PxPy 1. (6 points) Find Noel's Marshallian demands for donuts (x) and apples (y). Noel's income is $100 and the prices of donuts and apples are Pr = 2 and Py = 2. 2. (5 points) The government decides to introduce a tax on donuts of 2 dollars, that is after the tax the new price is Px = Pr + 2. Noel's mom wants her to have the same level of happiness as before the tax. Compute the transfer S that Noel's mom has to give her daughter so she is as happy as before the tax. 3. (6 points) Starting from the original income and prices: if the price of apples increases in 2%, by how much would the demand of donuts change? Are donuts and apples gross complements or gross substitutes? Hint: you can assume symmetry in the gross complementary - substitution relationship 4. (5 points) Using the Slutsky equation: What is the income effect on apples of a small increase in its own price? Your answer should be a function of Px, Py