Paul has preferences over the consumption of good I and of good 2 described by the utility function \"ate, z) = 0.25 ln(:1:) +0.75 ln(z). The unit price of good :1: is pm while that of good 2. is 30;. Paul's inc0me is y. a) Suppose that Paul's desired consumption bundle is a: : 2.5 and z : 1 and that his income is y = 8. How many units of z is Paul ready to give up to get an extra unit of :1: (at the margin) if he consumes this bundle? b) Suppose that pm : 2 and pz : 3. Is paul able to buy the consumption bundle in a)? How many units of 2: does Paul have to give up to get an extra unit of :1: (at the margin)? (3) Explain why Paul's desired consumption bundle is not optimal. Should Paul increase his consumption of at? Explain. Illustrate with a graph. (1) Find Paul's demand for good a" and demand for good 2 as a function of pm, pa, and y. e) Use your answer in d) to determine Paulis optimal consumption bundle when pm = 2, p2 : 3, and y : 8. f) Suppose that Paul's income falls by half. How will this affect Paul's consumption? Illustrate with a graph. Are good :1: and good 2: \"normal\" goods? g) Suppose that 1); falls to p; 2 1 (when 3; 2 8). Describe how Paulie consumption is a'ected by this reduction in pa. Illustrate with a graph