Paul consumes only 2 goods: melange [M] and water (W). The price of melange is 4 and the price of water is 2. Paul's income is 200. a. Write down Paul's budget constraint and graph it. (4 points} b. The price of melange changes to 2, and the price ofwater changes to 4. Write down Paul's new budget constraint, and graph it on the same graph below. (4 points) c. Suppose Paul considers melange and water to be perfect substitutes, and he is always willing to trade 1 unit of melange for 1 unit of water, or vice versa. That is, if Paul is maximizing utility, he must be consuming the largest total sum (M+W] possible. On your graph, show the bundle Paul would choose if his budget line is the one from part (a), and label this point C. (4 points) d. What bundle will Paul choose if his budget constraint is the one from part [b]? Show this point, and label it point D. (4 points) e. Draw one or more of Paul's indifference curves consistent with his choices in parts (c) and (d). (4 points) f. What would the prices of melange and water need to be for Paul to be maximizing utility while consuming 50 units of melange and 50 units ofwater? (5 points)