Kuhn tucker conditions and utility function, Macroeconomics

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1. Kuhn - Tucker Conditions

Max 2x + 3y

s.t. pxX + pyY ≤ M. x ≥ 0, y ≥ 0

2. Max (8 + x)(8 + y)

s.t. pxX + pyY ≤ M. x ≥ 0, y ≥ 0

Utility function

3. U(x, y) = x 1/3 y2/3

4. U(x, y) = 8x1/4y3/4

5.U (x, y) = min[2x, 3y]

Mux=

Muy=

MRS=

x* (Px, Py, m)=

y* (Px, Py, M)=

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