Assume that Deanna has the following utility function for grapefruit and can- taloupe: u(g,c) = g^0.3c^0.5. The price of a grapefruit, pg, is 5 and the price of a cantaloupe, pc, is 8. Deanna’s income is 160.
a. Find Deanna’s optimal consumption bundle. Show all of your work for the maximization problem, including a Lagrangian if appropriate
b. Assume that the price of a grapefruit falls to 4. Calculate Deanna’s demand for grapefruit and cantaloupe at the new price. Again, show work to support your answer
c. Calculate the compensated income, m′
d. What is the numeric value of the substitution effect? Solve for both goods
e. What is the numeric value of the income effect? Solve for both goods