Please answer all of questions 1 and 2 thanks!

Problem 1 - Indifference curves and MRS (17 points) Consider the following utility functions over consumption bundles r E R' representing the prefer- ences of individuals A through D, respectively, UA(X) = $1X2 UB(X) = X1 + Vx2 uc(x) = 2x1 + 12 Up(x) = min(X1, X2/2). 1. Indifference curves: (a) For individuals A, B, and C state the equation that represents the indifference curve with utility level equal to 2. That is, write r2 as a function of $1. (b) For individual D, state the indifference curve for utility level equal to 2 through state- ments of how a given r1 value maps to 12 value(s). Be careful to state the r1 domain of the indfifference curve. (c) Draw the utility level 2 indifference curve for each individual in separate diagrams with x1 on the horizontal axis and x2 on the vertical axis. 2. Marginal rate of substitution: (a) For individuals A, B, and C determine the marginal rate of substitution for any given bundle x. Furthermore, evaluate MRS in the bundle x = (2, 4). (b) Individual D is special in this context. I did not include D in the previous question. Explain why