Suppose a consumer's utility function is given by U(X, Y ) =X^1/2Y^1/2. Also, the consumer has $30 to spend. The price of X, PX = $3, and the price of Y, PY = $5.

a) How much X and Y should the consumer purchase in order to maximize their utility?

b) How much utility does the consumer receive?

c) Now suppose PX increases to $6. What is the new bundle of X and Y that the consumer will demand?

d) How much money would the consumer be willing to pay to avoid the price increase? Is this compensating variation or equivalent variation?

e) How much additional money would the consumer need in order to have the same utility level after the price change as before the price change? Is this compensating variation or equivalent variation?

f) Of the total change in the quantity demanded of X, how much is due to the substitution effect and how much is due to the income effect? Note: since there is an increase in the price of Good X, these values will be negative.