2. Consider an economy populated by a large number of farmers. indexed by i E (011}. Each farmer lives in a small island 1' and produces his own product. goods 1'. 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 indix'idual's production function is simply Y; = L. where L:- is the amount that the individual works and i; the amount he produces. For simplicity. utility take the form: U = C1- %L: where j- 3- 1., C;- is the consumption of aggregate goods. Suppose the demand for a given good depend on three factors: real income. the goods relative price. and a random disturbance to preference. which takes the form as: l; : 1" (%)*HEX1J[Z); In log terms. i.e.. yr=y+Er-'U(10-Pl- H>U where y is the log aggregate real income. 2;- is the shock to the demand for goods 2'. and n is the elasticity of demand across each individual good. 512- here denotes the 1 demand for good 2?. The shock 2 have a mean of zero across goods. i.e. / Zidt : l}. I] Also we assumed that z:- m .\\'[0.J). The log of the aggregate output is given by: 1 1 y = / yidr' = 131-. and the aggregate price level is dened as: p = f pidz' = g- 0 a (ID) Please interpret the above demand function for goods 3