John's utility function is given by the following equation

(, ) = min(3, 4),

where x is the unit of good X consumed, and y is the unit of good Y consumed. John's budget is $240, price of good X () is $5, and price of good Y () is $4. 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.

b) If increases from $5 to $6, what is the new optimal consumption (, )? Graph the new optimal consumption along with appropriate budget line and indifference curve on part a)'s graph.

c) If increases from $5 to $6 what is the substitution effect and income effect in terms of good X?