Suppose you are told that a consumer has the following utility function: U(qx, qy) = e (qy) ? 2qx ? 1. Their income is Y , the price of good x is Px, and the price of good y is Py. (a) (3 marks) Show that the Marginal Rate of Substitution is the same for U(qx, qy) as the positive monotonic transformation W = ln(U(qx, qy)). What type of utility function is W(qx, qy)? (b) (4 marks) Find q ? x , the demand for good x, and q ? y , the demand for good y. Hint: be sure to include information about where the function works. (c) (7 marks) Suppose you are given Px = $2 and Py = $18, provide a sketch of of the income-consumption curve for Y = {20, 25, 30, 35, 40, 45}. Be sure to label the points for each income and clearly indicate what is happening (i.e. values of qx and qy corresponding to each Y ). (d) (4 marks) Find the cross price elasticity of demand for q ? x and q ? y . Does this tell you anything about the relationship between the two goods?

2. (18 marks) Suppose you are told that a consumer has the following utility function: U ((13, qy) 2 cm?) x x/2qm 1. Their income is Y, the price of good 2: is PI, and the price of good 3,! is Py. (a) (3 marks) Show that the Marginal Rate of Substitution is the same for U ((15,, q,,) as the positive monotonic transformation W = ln(U(qm, 99)) What type of utility function is W(qm, qy)? (b) (4 marks) Find q; the demand for good as, and (1;, the demand for good 3;. Hint: be sure to include information about where the function works. (c) (7 marks) Suppose you are given P3 = $2 and Py = $18, provide a sketch of of the incomeconsumption curve for Y = {20, 25, 30, 35,40, 45}. Be sure to label the points for each income and clearly indicate what is happening (i.e. values of gas and q,, corresponding to each Y). (d) (4 marks) Find the cross price elasticity of demand for q; and (1;. Does this tell you anything about the relationship between the two goods