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The consumer’s Utility Function is U(x,y) = X1/2Y1/2. Further Px = $5 and Py = $10...

The consumer’s Utility Function is U(x,y) = X1/2Y1/2. Further Px = $5 and Py = $10 and the consumer has $500 to spend. The values of x* = 50 and y* = 25 maximizes utility.

The dual to the utility maximization problem is expenditure minimization problem where the consumer choose x and y to minimize the expenditure associated with achieving a specified level of utility. That is,

Choose x and y to Minimize Expenditure 5x + 10y subject to U = U(x,y) = X1/2Y1/2. Uo. Suppose Uo = 25.

Find x* and y* for the expenditure minimization problem above and check if the SOC is satisfied.

How much money will the consumer spend to gain Uo?

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