Callum eats only potatoes, p, and meat, m. One pound of potatoes contains 1,000 calories, whereas one pound of meat has 500 pounds. Callum prefers eating meat to potatoes, but in order to survive, he must consume at least 5,000 calories per week. a) Consider the following utility function: m U (p, m) = if 1,000p + 500m ≥ 5,000 -1 if 1,000p + 500m < 5,000 Give an interpretation of this utility function in words. Draw the indifference curves (they're not actually curves) associated with this utility function, being sure to label all slopes and intercepts. b) Suppose potatoes cost $1, meat costs $2, and Callum has $8 to spend. Argue that at his optimal bundle, Callum eats 4 pounds of potatoes (either graphically or algebraically). How many pounds of meat does he buy? Why does he not trade some of his potatoes in order to get more meat? c) Now the price of potatoes increases to $1.60 (while the price of meat and income remain the same). What is Callum's optimal consumption bundle under this set of parameter values? d) Plot the two bundles from parts (b) and (c) with the price of potatoes on the vertical axis and the quantity on the horizontal axis. Connect the two points. What can you conclude about demand for potatoes? What is the economic intuition for this result?
