A consumer's preferences are represented by the following utility function: u(ac, y) = $23; 10 1. Recall that for any two bundles A = (mA,yA) and B = (:1: 3,313) the following equivalence then holds AEBu(A) 211(3) Which of the two bundles ($1,111) = (9, 4) or (3:2, y2) = (4, 9) does the consumer prefer? 2. Take as given for now that this utility function represents a consumer with strictly convex preferences. Also remember that preferences are strictly convea: when for any three bundles AB, and C, ifB :AandCiAthen aB+(1a)C>Afor anya E (0,1). Use this information and your answer to part (1) to determine which of the two bundles ($3,313) 2 (7, 6) or ($2,112) 2 (4, 9) the consumer prefers. Verify your answer. 3. Derive an expression for the marginal rate of substitution. Interpret the M RS. What is the MRS at the point ($3,113) = (7, 6)? 4. Derive an equation for the indierence curve through the bundle ($2,112) = (4,9). With an equation it is meant: y as a function of 3:, y(:c), such that (m,y(:c)) lies on the indifference curve passing through bundle (4, 9)