Leo's utility function is U=min (3x,9.1y). If Leo's income is 171.1 dollars, the price of good X is 4 and the price of good Y is 6.2, what is Leo's maximum utility?

Assume that bob has a Cobb Douglas utility function U (F,H) = A F^0.7 H^0.3 over Food F and Housing H. How much does Bob spend on Housing and Food when the price of Housing is 10$ and income is 200 ?

Consider a consumer whose utility function is (screenshot) Assume the consumer has income $120 and initially faces the prices px=$1 and py=$1. How much x and y would they buy? Draw the budget constraint and the demands.

Question 1: Utility maximization and price index Tim consumes haircuts (₁) and sandwiches (x2). His utility function is: u (x₁, x2) = (x₁) (x₂)¹-0 The price of ₁ is p₁ and the price of x2 is p2. He has a total income of m. 1. Find Tim's demand function for goods 1 (x1 (P1, P2, m)) and 2 (x2 (P1, P2, m)), using a Lagrangian. 2. Suppose we'd want to compute a price index for the "average" good that Tim consumes. We define it as P such that: PV (p1, P2, m) = m where P is the price index, V(p1, P2, m) is the indirect utility that Tim can achieve when prices are p₁ and p2 and his income is m. Solve for the price level as a function of the individual prices, P(p1, P2), and show that it is equal to the inverse of the Lagrange multiplier in 1. Interpret. hint: the indirect utility is obtained by plugging the demand you found in (1) into the utility function: V(P1, P2, m) = u((x₁ (P1, P2, m), x2 (P1, P2, m)) 3. Does the price index satisfy homogeneity of degree 1? How does the im- portance of…