Question

D X-EC2010-1 M. 1. An individual consumer with Cobb-Douglas preferences over two products, x and y, maximises utility, U(x,y) = x1910, subject to the constraint that all income, M, is spent on x and/or y. Products x and y are priced at px and Py, respectively. (a) Set up the appropriate lagrangian for this maximisation problem, find the appropriate first-order conditions for this lagrangian and solve for X and y in terms of Px. Py and M. (40 marks) (b) For product x, find own price elasticity of demand, income elasticity of demand and cross-price elasticity of demand. Briefly interpret each of these three numerical results. (30 marks) (c) With respect to Cobb Douglas preferences more generally, what happens to the demand for each of two products (say, A and B) when the price of one product (say, product B) increases, as a result of the: () substitution effect; and, (II) income effect? Explain your answer(s) (30 marks) 2. (a) If leisure is an inferior good/product (over the relevant income range) for a particular individual, must that individual's labour supply curve be upward-sloping (over that income range)? Explain your answer. (30 marks) (b) Describe, using an incomes-in-two-periods indifference map and budget constraint framework (including the appropriate diagram(s)), how a borrower may respond, in terms of consumption (both today and tomorrow) and savings behaviour, to an increase in the interest rate. (30 marks) (c) Using the same framework as in part (b) above, is the borrower better off or worse off as a result of the increase in the interest rate? Explain your answer. (40 marks)

Answer 1

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