1. Derive Shepardis lemma and use it to show that the Slutsky matrix is symmetric.
2. 

... Assignment 1.pdf (1 page) 1 3 Q Q Search CAS EC 501 Microeconomics Assignment 1 Due 2/11/20 1. NS 3.4 (" As we saw in Figure 3.5,..") 2. An individual has the following preferences defined on consumption vectors x E R" : n u(x) = x4 where di > 0 and Cai = 1 i=1 i= 1 Her wealth is w E R+ + and the price vector is pe R* (a) Identify the constraint set X. (b) Solve the problem. (c) Discuss whether the necessary conditions are also sufficient. (d) Find the indirect utility function v(p, w) = maxxex u(x). 3. Let u : R4 - R be a continuously differentiable utility function satisfying the usual assumptions, and let f : R2 - R be a monotonic transformation of u. Consider the consumer problem of maximizing utility subject to the budget constraint. Show that the transformation f = f(u(x)) gives the same solution as u(x). Assume an interior solution. 4. NS 4.2 ("A young consumer has $600.....') 5. NS 4.4 ("Mr. Odde Ball enjoys commodities x and y....")