Paul has preferences over the consumption of good .1: and of good .2 described by the utility.r function u[2:,z} = [1.25 In[r]+.?5]n(e}. The unit price of good :1: is pI while that of good 2 is pz. Paul's income is y. a] Suppose that Paul's desired consumption bundle is :l: = 2.5 and z = l and that his income is y = 8. How man}.r Units of 2: is Paul ready to giVe up to get an extra unit of :c [at the margin] if he consumes this bundle? b] Suppose that p: = 2 and p: = 3. is paul able to buy the consumption bundle in a}? How mam}:r units of 2 does Paul have to give up to get an extra unit of 1 [at the margin]? c] Explain whyr Paul's desired consumption bundle is not optimal. Should Paul increase his consumption of 1:? Explain. Illustrate with a graph. d] Fin Paul's demand for good a: and demand for good 2 as a function of p31 p1. and y. e] Use your unsurer in d) to determine Paul's optimal consumption bundle when pI = 2. p; = 3, and y = 3. f] Suppose that Paul's income falls by hall". How 1will this sheet Paui's consumption? Illustrate with a graph. Are good u and good a \"normal\" goods? g] Suppose that p; falls to p; = 1 [when 3; = 3]. Describe how Paul's consumption is affected by this reduction in p... illustrate with a graph