Messi has 20 kilos of strawberries and 10 kilos of raspberries. Denote by S and R the quantities he consumes of strawberries and raspberries, respectively. These are the only goods, and their prices (in $/kilo) are: pR = 4, pS = 1.
a. Given his endowment, write the equation for the budget line. (Hint: start with the market value of his endowment.) With S on the horizontal axis and R on the vertical, draw this budget line and call it BL1. Mark its slope and vertical intercept (the horizontal intercept is optional).
b. Suppose pS rises to 2. Draw the new budget line and call it BL2. Show its slope and vertical intercept (horizontal intercept is optional)
c. Suppose his utility function is U = min{S, R}. Does he gain or lose after pS rises to 2? Explain briefly, and illustrate with two ICs showing his old and new consumption points.
d. Suppose, instead, his utility function is U = min{S/3, R}. Does he gain or lose after pS rises to 2? Explain briefly, and illustrate with two ICs showing his old and new consumption points.
e. Suppose that, instead, his utility function exhibited convex ICs, and initially (with BL1) he consumed S > 20. Would he gain or lose after pS rises to 2? Explain briefly.