Consider an agent who want to maximize her utility function, g, 92) = c1 c2 subject to the budget constraint, c1 +pc2 = wwith c1, 02 > 0 indicating consumption of commodity i and 2, respectively, while p > O and w> U are exogenously given parameters. indicating the relative price of good 2 and the relative wealth in term of good 1's pride. Decide whether the following claims are true or false. w - The value of the Lagrange multiplier is A a. C" False i] True _ w2 ' The value function ulw) is equal to 1104/) = E. False True Consider an agent who want to maximize her utility function, u (C1, C2) = 1 2 Subject to the budget constraint, c, + pc2 = w with C1, C2 > 0 indicating consumption of commodity 1 and 2, respectively, while p > 0 and w> 0 are exogenously given parameters, indicating the relative price of good 2 and the relative wealth in term of good 1's price. . . . O False O True w . The value function u(w) is equal to u(w) = 4p O False O True . )(w) measures the approximate change in utility that can be obtained from an increase/decrease in wealth w. O True O False