4. Suppose that we represent Richard's preferences for pounds of coffee(the x-good) and donuts(y-good) with the utility function u = x + y^(1/2). The Marshallian demand functions associated with this utility function are given by the following demand functions: x = I/Px - Px/4Py and y = (Px/2Py)^2 where Px and Py are the prices of a pound of coffee and a done respectively and I is the income he will spend per month.

a) If Px= $12, Py= $1and I = $120then how many pounds of coffee and donuts does he demand? Illustrate his best bundle and label the bundle A.

The government decides to subsidize coffee consumption. The subsidy is set at $4per pound.

b) What will be his best bundle after the subsidy lower the price to $8? Illustrate his new budget line and best bundle in your diagram. Label the best bundle B. What is the level of his utility at bundle B?

c) How much did the subsidy cost the government? Illustrate these costs in your diagram.

One way to implement a subsidy is to give consumers vouchers that can be used like money towards the purchase of a certain good. To implement the above subsidy, the government would distribute vouchers with a face value of $4.

Each voucher is good for $4 off of the price of a pound of coffee. For simplicity assume that the vouchers are divisible (eg 0.5 vouchers is good for $2 off the price of a half-pound of coffee). In part (b) above, you showed that Richard will purchase 13 pounds of coffee at the subsidized price. For the remainder of the question, assume that the government gives him 13 vouchers with a face value of $4.

d) Assume that Richard can neither buy additional vouchers nor sell any of his 13 vouchers. In a new diagram, illustrate his new budget set. Indicate in your diagram, bundle B from your previous diagram and draw an indifference curve through B.

e) Assume that Richard can sell any of his 13 vouchers at face value. Will he choose to do so? Briefly explain your answer (your answer must refer to his MRS to receive credit). Illustrate the budget line generated by his ability to sell vouchers in the diagram for part (d).

f) Find Richard's Hicksian demand functions as a function of prices and utility level.

g) Use your Hicksian demand functions to find a bundle, C, such that

1) Richard is indifferent between C and B;

2) Richard would choose bundle C at the original prices.

What is the cost of bundle Cat the original prices? Illustrate C in your indifference curve diagram for part (c)

h) What is the lowest price at which Richard would be willing to sell all of his vouchers? Briefly explain your answer.

i) What is the value of equivalent variation to the subsidy? Illustrate the value of equivalent variation measured in donuts in your indifference curve diagram for part (d)