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James consumes two goods, X and Y. James has a utility function given by the expression: U = 4Xo.5y().5 The current prices of X and Y are 25 and 50, respectively. James currently has an income of 750 per time period. (a) Write the marginal utility functions for both good X and Y. (4 marks) (b) Write an expression for James's budget constraint. (2 marks) (c) Calculate the optimal quantities of X and Y that James should choose, given his budget constraint. (8 marks) ((1) Suppose that the government rations purchase of good X such that James is limited to 10 units of X per time period. Assuming that James chooses to spend his entire income, how much Y will James consume? Is James satisfying the usual conditions of consumer equilibrium while the restriction is in effect? Explain your answer (compare James's utility with and without ration restriction). (6 marks)