1. Consider the instantaneous utility function E L'I'i 1+E(h't)s Ut:1n(ct)qr where: U: denotes instantaneous utility; c: denotes consumption (a variable); ht denotes labor (a variable); 7,5 > 0 are parameters; and 1' denotII time- '1! (the greek letter \"garnma\") is simply a scaling parameter; and e (the greek letter \"epsilon\") is the Frisch elasticity of labor supply. In particular, the Frisch elasticity tells you by how much labor supply changes in percent terms given a 1 percent increase in the wage1 everything else held constant. This concrete functional form for instantaneous utility is one of the most widely used in Macroeconomics and International Macroeconomics- (a) Of course, in this case we can think of u(q) : ln(ct) and com) : 7%(h1):_ Derive mathematically a', a"; e', v\" and state what their signs are equal to (i.e.; positive or negative). (b) What is the economic interpretation of u' and v"? (c) Derive mathematically the total derivative of instantaneous utility