Given preferences represented by the utility function U(x 1 , x 2 ) min 3x 1 , x 2 , lets figure out the following Demand for x 1 and x 2 for perfect complements Let m 100, p 1 2, and p 2 4 Find the quantities demanded for x 1 and x 2 Suppose p 1 increases to p 1 10 Now what is the optimal bundle D...

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Given preferences represented by the utility function U(x 1 , x 2 ) = min{3x 1 ,

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Given preferences represented by the utility function U(x₁, x₂) = min{3x₁, x₂}, let’s figure out the following:

Demand for x₁ and x₂ for perfect complements.
Let m = 100, p₁ = 2, and p₂ = 4. Find the quantities demanded for x₁ and x₂.
Suppose p₁ increases to p₁ = 10. Now what is the optimal bundle?
Decompose this change into the income and substitution effects.
Your sister has just promised to send you pocket money of $500 each month starting next month and she will keep doing it forever. What is the present value of “having such a sister” if monthly interest rate is equal to 1% (one number)?