Consider an economy in which two goods, manufactured goods M and services S, are consumed. Suppose the representative consumer in the economy has preferences Each of the two goods is produced using labor only, with Show that the household will consume U (FM.ES) = (FN + F) IM = VM = ys Let pu.ps be the prices of manufactured goods and services relatively and let w be the wage rate. Suppose the total supply of labor is normalized to 1. 1. The household's problem is to maximize utility by choosing how much to consume of each good. That is, it solves 27 max M.S subject to 13 PM AMEM Asls +1. PMFM+PSTg = w and Is = Ps - where p= (p+p). To do this, you can follow the following hints. Set up a Lagrangian and take FOCs. Divide one FOC by the other to show that I/Is= (PM/Ps)*. in the budget constraint and solve for rs. Use this equation to substitute for r 2. Argue, either mathematically or intuitively, that the only way both industries will hire a positive amount of labor is if PMAM = W = PSAs Hint: Suppose u> psAs. What is the optimal amount of labor for a firm in the S sector to hire?