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John earns $120 per week and likes to consume wine and cheese. His utility function is...

John earns $120 per week and likes to consume wine and cheese. His utility function is of the form ?(?, ?) = (? ^1/2)(? ^3/2) where x denotes the amount of cheese consumed and y the amount of wine. His marginal utilities are ??? = (? ^3/2) / (2? ^1/2) and ??? = (3? ^1/2)(? ^1/2) / 2

d. The price of a bottle of wine is $10 and the price of a piece of cheese is $3.

What is the optimal bundle for John using the Marshallian Demands?

What is the utility level, ?̅?

e. Using the prices in part d, and the utility level, ?̅, solve for the optimal bundle with the Hicksian Demands.

f. Using the prices and the utility level from part d, calculate the expenditure.

g. The price of cheese goes up to $5 a piece. What is the new optimal bundle with an income of $120? What is John’s utility now?

h. Find the equivalent and compensating variation for John when the price of cheese rises to $5.

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