Mark's preferences are given by U=6F xM x1, where F is food, M is manufacturing good and I is leisure per week. His total time endowment (after sleep) is 72 hours per week. Prices of F and M are $6 and $4 respectively. His hourly wage is $10 (a) What is Mark's weekly equilibrium consumption of goods and leisure? (HINT: you need to use any two tangency conditions out of three). (b) If the government taxes his wage at the rate of 20%, what is his equilibrium consumption of goods and leisure? What is the tax revenue collected from Mark? (c) If instead of the wage tax of 20%, the government imposes a lump-sum tax on Mark's weekly income that collects the same revenue as in (b). What is his consumption of goods and leisure now? (d) Looking at your results in (b) and (c), why does leisure drop in (c) but not in (b)? Explain using the effects and the type of the good involved. Why do F and M drop by less in (c) as compared to (b)? Briefly explain. au 4F1 MU-20-6xxx=24 180-2--and F MUM = = 6x xl=- F OF M MU = - au XFxM1=6FM. al =