Part I. Consumer Theory and General Equilibrium (40 points) I. Model 1. Specify two goods. For example: food F and clothing C 2. Specify two consumers' utility functions. For example: 41 (F, C) = FO.5C0.5 U2 (F, C) = F04C0.6 II. Analysis 1. For each consumer i, i = 1, 2, solve the following problems. a. Draw an indifference curve by connecting multiple consumption bundles. b. Derive the marginal rate of substitution (MRS) from the utility function. c. Given the prices, PF, Pc, and the income , express and draw the budget constraint. d. Solve the optimal consumption bundle as functions of PF, Pc, and It. e. Derive and draw the individual demand curve for each good. f. Illustrate the substitution and income effect for each good caused by an increase in own price. 2. Consider a pure exchange economy between consumers ] and 2 with the above two goods. a. Draw the Edgeworth box, and specify each consumer's endowment of each good. b. Show whether the endowment point is Pareto efficient or not. If not, show the area where there can be mutually beneficial trade with respect to the endowment point. c. Derive and draw the contract curve in the Edgeworth box. d. Suppose the economy is in a competitive equilibrium, solve the equilibrium consumption bundles as functions of the price ratio and total endowments