A consumer has utility u(x1, x2) = 2x2 + x1 Normalize the price of good 2 to 1 and let pj be the price of good 1 and m the consumer's income a) Find the consumer's marginal rate of substitution b) Find the consumer's optimal choice for p=1 and m=8 c) Obtain the consumer's optimal demand as a function of p1 and m d) Assume p=1 and m-8 (and as always price of good 2 is normalized to 1). Suppose the store where the consumer buys good 1 offers a Black Friday discount: price of good 1 is 1/4 on the first 4 units bought. What is the consumer's optimal choice now? Also, assuming the following week the consumer has the same preferences and a new m-8 income to spend, how much, at most, would she be willing to pay in order to keep the discount in place? (Hint: draw carefully the budget line}