3. Lu likes to go to the beach and to play golf. His preferences over beach trips (x) and golf outings (y) can be represented by the utility function: U = (x^(1/2), y^(1/2)). The demand functions associated with this utility function are x = 2/Pxand y = 2/Py. Finally suppose that the price of a beach trip is $8, the price of a golf outing is $10 and that Lu has $400 to spend.

a)Putting beach trips on the x-axis and golf outings on the y-axis illustrate Lu's budget set.

The local government needs to raise revenues. One way to do so would be to impose a per-unit tax. Suppose that the government levies a $4.50 tax on beach trips (so the price rises to $12.50).

b) In your diagram for part (a) illustrate Lu's new budget set.

c) Using the demand functions find Lu's best bundle on his new (post-tax) budget line. Illustrate the best bundle and an indifference curve through the bundle in your diagram from part (a).

d) What are the tax revenues? Illustrate the tax revenues in units of golf outings in your diagram.

An alternative to a per unit tax would be to levy a fixed fee such as a license. In particular, the government could require that Lu purchase a license to go to the beach. The prices of beach trips and golf outings would remain at their original values, 8 and 10 resp.

e) Suppose that the price of the license was set equal to the tax revenues that you found in part (e). Assuming that he buys the license, illustrate Lu's budget line in your diagram above.

f) Will Lu be better or, worse off or the equally well off buying the license as he was when there was a per unit tax? Briefly explain your answer. To receive full credit you must refer to his MRS.

From your answers above it follows that the government can set the price of the license higher than the tax revenues from part (d) and make Lu no worse off. Let F be the price of the license such that Lu is no better nor worse off than he was with the per-unit tax. Below you will determine the value of F.

g) Redraw your budget set from part (b) below. Include in your diagram your per-unit tax budget line from part (c), and the best bundle and indifference curve from part (d). Illustrate the budget line associated with the license fee of F.

h) Find the Hicksian demands for the indifference curve through your best bundle from part (d) and the original prices.

i) Illustrate the Hicksian demands in your diagram for part (6).

j) Use the Hicksian demands to calculate the value of F.

k) What is the equivalent variation to the per unit tax?