Chris Jordan’s diet consists only of Whoppers and Hawaiian Punch. Chris has $160 to spend on Whoppers and Hawaiian Punch and each Whopper costs $2 and each gallon of Hawaiian Punch costs $4. Let W be the number of Whoppers Chris eats and H be gallons of Hawaiian Punch. His happiness is measured by the utility function u(W, H) = 10WH. a. Set up the Lagrangian for Chris's constrained utility maximization problem.
b. Using differential calculus and algebra, use the Lagrangian in A to find how many Whoppers and gallons of Hawaiian Punch Chris should buy if he wishes to maximize his utility subject to the constraints on his purchasing power. What is the value and interpretation of the Lagrange multiplier for this problem?
c. How much utility is attained with the original utility maximizing amounts of Whoppers and Hawaiian Punch?
d. Suppose that the price of Whoppers now increases to $4 with the price of Hawaiian Punch and income constant. Find the new utility maximizing amounts of Whoppers and gallons of Hawaiian Punch. (Use the simultaneous equations method
e. Determine the decomposition basket for the substitution effect due to the change in the price of Whoppers. (Use simultaneous equations)
f. Find the numerical values of the income and substitution effects of the change in the price of Whoppers measured in terms of Whoppers.
g. Are Whoppers a normal, or an inferior good? Justify your answer.