There are two goods in the world, pumpkins (x1) and apple cider (x2). Pumpkins are $2 each. Cider is $7 per gallon for the first two gallons. After the second gallon, the price of cider drops to $4 per gallon.
a) Peter's income is $54. Draw his budget line. Solve for the intercepts on the x1 and x2 axes, and the kink in the budget line.
b) Peter's utility function is u(x1,x2)= x1 + 3(x2). Find Peter's optimal consumption bundle.
c) Paul's income is $22. Draw his budget line. Solve for the intercepts on the x1 and x2 axes, and the kink in the budget line.
d) Paul's utility function is u(x1,x2)= min (3x1,2x2). Find Paul's optimal consumption bundle.