Instructions: Complete this problem set individually and show your complete solutions. You can use MS Word, LaTeX or R Markdown, then compile it and submit it to the VLE classroom. If you prefer writing your answers by hand, then box your final answers, and take a clear photo of your solutions and answers. Submit it as a PDF document. Those who will be caught performing intellectual dishonesty will be given a zero (0) for this requirements 1. Labor Supply Consider the decision of Mark who works on a day-to- day basis and gets paid PhP 60/hr at work. Mark's preferences can be described by the utility function: U-C0.5L0.5 Where C represents his consumption expenditure (earned all through paid labor) and L is leisure hours. Assume that Mark divides his day only between labor and leisure. Derive his marginal utility of consumption and leisure. b. Compute for the optimal number of work hours. c. Assume that Mark becomes endowed with an unearned income of PhP 240/day because of government benefits. What happens to optimal leisure hours? d. Suppose that Mark's wage increases from PhP 60/hr to PhP 80/hr (while still receiving PhP 240/day non-labor income). How much will he spend for labor and leisure? e. Based on the change in labor hours of Mark, what can you infer about the income and substitution effects? 2. Labor Demand Suppose that Confidential Funds (CF) Bakery has the following Cobb-Douglas Production Function: Q=KE Where K represents the units of capital employed, E is the total number of employee hours hired, and Q is total outputs produced. CF Bakery is bound by the minimum wage of the land and pays PhP 50/hr and the cost of capital r, is equal to PhP 1000 per unit. The firm initially faces 2 units of capital which cannot be changed. a. If CF Bakery currently employs 8 hours of labor, calculate the total cost and marginal cost of the firm. b. Calculate the marginal products of labor and capital. c. Calculate the Marginal Rate of Technical Substitution. Is CF Bakery behaving optimally? Why or why not? d. Suppose that instead of employing 8 hours of labor, the firm instead hires 24 hours of labor. Compute for the new marginal products of labor and capital. Calculate the new MRTS. Is CF Bakery behaving optimally with this new number of hired employee hours? Why or why not? 3. Labor Market Equilibrium and Elasticities. Suppose that the demand for restaurant waiters in a small city is defined by the function E- 160-20w, where E is the number of waiters and w is the wage in dollars per hour. Meanwhile, the supply for the restaurant waiters in that city is E-40+30w. a. Find the equilibrium wage and employment. b. What is the wage-elasticity of demand for restaurant owners at the equilibrium wage? Is the demand curve elastic or inelastic? The wage elasticity for demand is -1 which means that restaurants' demand is inelastic. There is no significant effect on the increase in wages (1% increase) because the effect in demand (1% decrease) is the same magnitude. C. . Suppose that the government puts in place a minimum wage of USD 6 per hour. How does this affect employment level of restaurant waiters in the city? d. Suppose that after the imposition of the minimum wage in the city above, all of the waiters who lose their jobs (your answer from the previous question) opted to work in another sector, say grocery store cashiers. The demand and supply for that sector are defined by the function L =200-20w, and L =-100+80w. What happens to wages and employment in the market for grocery store cashiers? Graphically illustrate the D effects in that market.