Kindly solve the following

4. Compute the utility of a worker. How is it affected by total productivity (as measured by L) and overhead costs? We now modify the model and assume that each worker is also endowed with q units of managerial quality. A firm employing a manager of quality q has a total overhead cost now equal to 1/q (instead of just 1). q is uniformly distributed in the population over [9min, 9max], i.e. with c.d.f. F(q) = -9min 9max -9min and density f(q) = F'(q) = = 1 4max - 9min -. Each worker has to work either as a worker or a manager, and can't do both. There is free entry of firms which compete to hire managers. Let w(q) be the wage paid to a manager with quality q in equilibrium. 5. Show that (with the same price normalization as before), one must have w(q) = 1/b - wl/qConsider the following economy. There is continuum of workers with mass 1, each endowed with L units of labor, and a continuum of goods of mass N. They have the same utility given by -bei U = b -di, where / is the number of goods, which is endogenous. Each differentiated good is produced by a monopoly. There is a fixed overhead cost equal to / units of labor. There is no variable cost (an arbitary large quantity of the good can be produced: these goods are like software, music, etc). 1. Show that if the price of good i is pa, then the demand for good i by a consumer with income R is 4 = c- -In pa, where C= R + + So p; In p.di So pidi 2. Show that each firm will charge a price p; = p = ebc-1, where c is defined as above and common to all workers. N is endogenously determined by the free entry condition. We normalize the common price level to p = 1. 3. Compute the wage level w (as defined by the wage of 1 unit of labor, so that a worker's income is wL). How does it depend on the overhead labor cost I? Explain why