Consider an economy with three goods. Suppose that a consumer has a continuous utility function satisfying local nonsatiation. Suppose also that the consumer's Walrasian demands for goods 1 and 2 when p3 = 1 satisfy 331(33'13132, 1: W) = a1 + 51391 + C1P2 + d1p1P2 5132(piap2a 1: W) = a2 + 52101 + C2392 + d2P1P2 (a) State Walras' law and use it to nd the Walrasian demand for good 3. (It's ne to just give the demand when p3 = 1.) (b) State a result about the homogeneity of Walrasian demands and use it to nd the consumer's Walrasian demands at other values of p3. (c) Note that the Walrasian demands for goods 1 and 2 are independent of wealth. Show that this makes it very easy to nd the Hicksian demands for goods 1 and 2. State the Compensated Law of Demand. Show that this law puts some restrictions on the possible values for (:11, b1, (:1, (171,32, b2, (:2,d2). (d) Dene the Slutsky substitution matrix. What properties must it have if demands are derived from maximizing a continuous, locally nonsatiated, and strictly quasiconcave utility function? Give at least one additional restriction on (:11, b1, (:1, (1,132, 52,62,132\" that this implies