Units of A Units of B 16 6 12 8 8 12 4 24

Q5. Jason has preferences defined over novels (good x) and DVDs (good y) described by the utility function U(x,y)= x2y2. He has an income of $120; novels cost $5 each, while DVDs are priced at $15 each. [Hint: MUx=2xy2, MUy=2x2y]    a) Sketch Jason's budget constraint, indifference curves and the interior solution in a graph. b) Calculate Jason's optimal consumption bundle, and his maximized utility level.   Suppose the price of novels increases to $7.5, while the price of DVDs and income are unchanged.   c) Calculate his new optimal bundle, show it in the same graph from a), and interpret the Marginal Rate of Substitution (MRS) at this new optional bundle (point).

Emily is a utility maximizer. Her income is $100, which she can spend on cafeteria meals and on notepads. Each meal costs $5 and each notepad costs $2.  At these prices Emily chooses to buy 16 cafeteria meals and 10 notepads. a) Draw a diagram that shows Emily’s choice using an indifference curve and her budget line, placing notepads on the vertical axis and cafeteria meals on the horizontal axis. Label the indifference curve, I1, and the budget line BL1.  Make sure you calculate the endpoints of the budget constraint. b) The price of notepads falls to $1; the price of cafeteria meals remains the same. On the same diagram, draw Emily’s budget line with the new prices and label it BL2.  c) Lastly, Emily’s income falls to $90. On the same diagram, draw his budget line with this income and the new prices and label it BL3. Is she worse off, better off, or equally as well off with these new prices and lower income than compared to the original prices and higher income?

Suppose the utility function of U(x1, x2) = x11/2x21/2 and the budget constraint of p1x1+p2x2=m. Let’s assume that p1=$1.5, p2=$2, and m=$60. Find the optimal bundle. Also, specify the optimal bundle.