In: Economics
John’s utility function is given by the following equation
?(?, ?) = min(2?, 5?),
where x is the unit of good X consumed, and y is the unit of good Y consumed. John’s budget is $140, price of good X (? ) is $3, and price of good Y (? ) is $10. Show all the steps, with definition of every new notation used in the steps.
a) What is John’s optimal consumption (?∗, ?∗)? Graph the optimal consumption along with appropriate budget line and indifference curve. (7 pts.)
b) If ? decreases from $3 to $2, what is the new optimal consumption (? , ? )? Graph the new optimal ???
consumption along with appropriate budget line and indifference curve on part a)’s graph. (7 pts.)
c) If ? decreases from $3 to $2 what is the substitution effect and income effect in terms of good X? (5 pts.) ?