3. A consumer has the following utility function U (x, y, z) = x + y+...

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3. A consumer has the following utility function U (x, y, z) = x + y+ z. He must maximise his utility subject to his budget constraint m 2 Pzx + Pyy + Pzz and non-negativity constraints x > 0, y 2 0 and z 2 0. a. Write out the Lagrangian for this maximization problem b. Write the first order conditions for this problem. c. Find the optimal values of consumption of x, y and z conditional on values of the exogenous variables (px. Py, Pz, m). Clearly state which of the constraints are binding in each case. %3D 3. A consumer has the following utility function U (x, y, z) = x + y+ z. He must maximise his utility subject to his budget constraint m 2 Pzx + Pyy + Pzz and non-negativity constraints x > 0, y 2 0 and z 2 0. a. Write out the Lagrangian for this maximization problem b. Write the first order conditions for this problem. c. Find the optimal values of consumption of x, y and z conditional on values of the exogenous variables (px. Py, Pz, m). Clearly state which of the constraints are binding in each case. %3D