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A utility function is given by u(x1, x2) = min{x1 + 2x2, 3x1 + x2}

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A utility function is given by u(x1, x2) = min{x1 + 2x2, 3x1 + x2}.

(a) Graphically determine the optimal consumption for the following prices and income: p1 =1, p2 =1,I =30.

(b) Suppose the price of good 2 increases to p2 = 3. Determine graphically the change in consumption of goods 2 and 3. p1 = 1, p2 = 2, I = 20.

(c) Determine the least costly consumption bundle which gives the consumer the same utility as in (b) when prices are p1 = 1, p2 = 1, i.e., Determine the Hicksean demand.