Consumption tax. (40 points) Consider an economy in which there are L workers and each workers' utility is 12 u(c,h)=log c2h , where c is consumption and h is the number of hours worked. The worker pays a consumption tax for every unit of the good she purchases but no income taxes. Her budget constraint is thus (1 + )c = wh. Firms in this economy operate with a constant returns production function that uses only labor: Y = H, where H is the total number of hours of work the firm hires and Y is the amount of output it produces. The firm's objective is to maximize its profits, given by Y wH