1. A consumer wants chicken nuggets for dinner and they are deciding between going to Mcdonald's or Burger King. They receive a constant amount of utility from each nugget, but they prefer McDonald's nuggets, so their utility function is U(M, B) - 5M + 4B (a) Show that the consumer is indifferent between consuming 4 Mcdonald's nuggets (and 0 BK nuggets) or 5 Burger King nuggets (and 0 Mcdonald's nuggets) (i.e. show that these two consumption bundles give the same amount of utility). Show that they are not indifferent between consuming 5 McDonald's nuggets or 4 Burger King nuggets (which do they prefer?) (b) Assume that the consumer has $20 to spend on nuggets and BK nuggets cost $1 each while McDonald's nuggets cost $2 each. Draw the consumer's budget constraint on a graph with B on the y axis and M on the x-axis. Make sure to label the intercepts. (c) How much utility would the consumer get if they spent all of their income on Mcdonald's nuggets? On the same graph as above, draw an indifference curve for this level of utility. Repeat assuming they instead spent it all on BK nuggets. Which choice gives the consumer more utility? Could they do better than this choice? (d) What is the slope of each of the lines you drew above? How does the slope relate to their optimal choice? What is the Marshallian demand for each good? (e) Instead of spending a fixed amount of income on nuggets, the consumer instead wants to reach 100 units of utility. Assuming the same prices as above, what is the cheapest way they can achieve this level of utility (i.e. what is their Hicksian demand)? How much does it cost the consumer to achieve this level of utility? (f) Mcdonald's is considering changing the price of its nuggets. What is the highest price they could charge where this consumer would buy their nuggets instead of Burger King's (you can assume if they are indifferent they will buy Mcdonald's)? 2. A consumer is making peanut butter and jelly sandwiches. Each sandwich requires 1 ounce of jelly (J) and 3 ounces of peanut butter (P) and a completed sandwich gives the consumer exactly one utility (you can assume they have unlimited bread already). The consumer does not get any utility from peanut butter and jelly on their own. (a) What does this consumer's utility function look like? (Hint: Make sure plugging in J=1 and P-3 gives exactly one utility) (b) Explain why U - min(3.), P) also represents this consumer's preference. How much utility does each sandwich give in this case? (c) Draw an indifference curve for the utility function in part b. (d) Assume that the consumer has $5 to spend on peanut butter and jelly sandwiches, the price of peanut butter is $0.20/oz and the price of jelly is $0.40/oz. How much does each sandwich cost? How many sandwiches can the consumer make given their budget. How many ounces of peanut butter and jelly will they buy? (e) If the price of peanut butter increased, what happens the consumer's consumption of peanut butter (increase, decrease, or stay the same)? What happens to their consumption of jelly? (f) Now assume that the consumer instead wants to achieve a total of 15 utility (using the utility function from part b). How many sandwiches do they need to make to achieve this level of utility? How many ounces of peanut butter and jelly do they need to make this many sandwiches
