Question: 2. (18 marks) Suppose you are told that a consumer has the following utility function: U(qx,qy)=e(qy)2qx1. Their income is Y, the price of good x

2. (18 marks) Suppose you are told that a consumer has

2. (18 marks) Suppose you are told that a consumer has the following utility function: U(qx,qy)=e(qy)2qx1. Their income is Y, the price of good x is Px, and the price of goody 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 qx, the demand for good x, and qy, 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 qx and qy. 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(qx,qy)=e(qy)2qx1. Their income is Y, the price of good x is Px, and the price of goody 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 qx, the demand for good x, and qy, 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 qx and qy. Does this tell you anything about the relationship between the two goods

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