2. Suppose you are told that a consumer has the following utility function: U(qm,qy) = emu) >

2. Suppose you are told that a consumer has the following utility function: e(qy) X 1. Their income is Y, the price of good is Px, and the price of good y is Py. (a) Show that the Marginal Rate of Substitution is the same for U(qx, qy) as the positive monotonic transformation VV = qy)). What type of utility function is VV(qx, (ly)? ( b ) 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 ) 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 qc and qy corresponding to each Y) ( d) Find the cross price elasticity of demand for and q*y. Does this tell you anything about the relationship between the two goods?