Question 4 11 Marks {0.5, 0.5, 2. 5. 3) A consumer has the following utility function U (x1. x2) = x1{x2+ 4) Prices of the two goods X1 and x2 respectively are p. and p2 and the consumer has income m. We assume that all prices and income are strictly positive- Furthermore, throughout this question we assume that m > 4p2. (a) (0.5 marks) Find the consumer's MRS between the two goods (i_e_, marginal utility of x1 divided by marginal utility of x2}. (b) (0.5 marks) Write down the equation for the consumers budget line and the slope of the budget line where X1 is on the horizontal axis and x2 is on the vertical axis. (c) (2 marks) Solve the consumer's optimization problem and express the demand for the two goods in terms of prices and income.(d) (5 marks) Consumer expenditure data in developing countries show that individuals I: spend more than half of their income on food a proportion of income spent on food declines as income increases- (i) (2 marks) Can either of the two goods x1 or x; represent food? Explain your answer. (d) (5 marks) Consumer expenditure data in developing countries show that individuals I: spend more than half of their income on food a proportion of income spent on food declines as income increases- (i) (2 marks) Can either of the two goods x1 or x; represent food? Explain your answer. (ii) (3 marks) Compute the missing values of elasticities in the following table assuming M = 10, p1 = 2, and p2 = 1. Income elasticity | Absolute value of own price elasticity ' Cross price elasticity (e) (3 marks) While X2 is produced locally. X1 is transported from a different region. Assume p2 = 1. Building a new railroad {that connects the regions) will reduce transportation cost which in tum will reduce the price of good 1 from p1 = 210 p1 = 1. Railroad will be funded by taxes which will reduce each consumer's disposable income from m = 10 to m = 10 T. A utility-maximizing consumer will accept higher taxes as long as T5