2. Consider an economy populated by a large number of farmers. indexed by i- 6 (0,1). Each farmer lives in a small island 1' and produces his own product. goods 2". Individuals produce goods using their own labor. sell their output in competitive market at price H. and use the proceeds to buy an aggregate goods at price P. Consider a representative producer of a typical good. goods i. The individuals production function is simply Y1- : L. where L:- is the amount that the individual works and l; the amount he produces. For simplicity. utility take the form: C.- : C:- HAIL: where j. > 1., C;- is the consumption of aggregate goods. (3.) Piease rst set up individuals maximization problem. Letting lower case letters denote the logarithms of the corresponding upper-case variables. i.e.. E1- : logLi. 512- = logii. etc. Show that the individual's labor supply is given by: 1 71 t=a= (am Please interpret it