microeconomics

Scott derives utility from only two goods, Coke Zero (C) and loud music {M}. His utility function is as follows: U(C,M) = CM Scott has an income (I) of $100 and the price of Coke Zero (Pc) and loud music (Pm) are both $2. a. What quanties of C and M will maximize Scott's utility? b. Suppose that a tax of $1 per unit is levied on soda: assume all of this cost is paid by the consumer. What is Scott's new utility maximizing market basket of goods? c. Suppose that, instead of the per unit tax in (b), a lump sum tax of the same dollar amount is levied on Scott. To be clear: this is the total tax amount (not necessarilyjust $1) from part (b). What is Scott's utility maximizing market basket? d. The taxes in (b) and (c)I both collect exactly the same amount of revenue for the government. Which of the two taxes would Scott prefer? Show your answer numerically and explain why Scott prefers the per unit tax overthe lump sum tax, or vice versa, or why he is indifferent between the two taxes