There are 1000 consumers in an economy that each have the same utility function given by u (c, l) = 2√c − 4(1 − l)^2 where c is their consumption and l is the percentage of time they devote to leisure. a single firm serves the market with production function y = √12000l^1/2k^1/2. the firm cannot choose its capital stock, which is fixed at k = 256. you can assume the price level is equal to 1 so real and nominal wages are equivalent. a. solve for an individual consumer’s labor supply as a function of the real wageb. what is the total supply of labor hours for the economy in one day as a function of the real wage (hint: remember you have just solved for labor supply as a percentage of one consumer’s time. there are 1000 consumers and each one has 24 hours they can work)c. solve for the firm’s labor demand as a function of the real waged. what is the equilibrium real wage and equilibrium total number of hours worked per day? how many hours does each consumer work per day? e. what is total output for the economy? (note: your numbers won’t necessarily come out very nicely for these questions - round to 2 decimal places)f. the government wants to increase the equilibrium real wage, so it mandates a minimum wage of $15 per hour. what happens to labor supply and demand? how many total hours will be worked? what is total output? g. now the government gets rid of the minimum wage and tries a wage subsidy instead (i. e. they pay the consumer some amount for every hour worked). how large does the subsidy have to be in order to reach $15/hr? (don’t forget that the equilibrium wage will change with the subsidy) now how many hours will be worked and what is total output?