8. A consumer has the following utility maximization problem Maxx,y U(x, y) = x(y + 1)...

 

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8. A consumer has the following utility maximization problem Maxx,y U(x, y) = x(y + 1) s. t. B = Pxx+Pyy Where x, y are the two consumption goods whose prices are px and py, respectively. Her budget is B. a) From the first order conditions (FOCs) find expressions for the demand functions x* = x(px, Py, B) and y* = y(Px, Py, B) = b) Find an expression for the indirect utility function U* au* U(Px, Py, B). Verify that λ* = ав The consumer's utility maximization problem could be recast as the following Minimize pxx+Pyy s.t. U* = x(y + 1) c) Find the values of x and y that solve this minimization problem from FOCS d) Now suppose the SOCs are automatically satisfied so you do NOT have to check them. Derive the expenditure function E* = E(Px, py, U*) and show that the values of x and y that solve this minimization problem are equal to the partial derivative of the expenditure JE* JE* function, i.e. and respectively. apx apy 8. A consumer has the following utility maximization problem Maxx,y U(x, y) = x(y + 1) s. t. B = Pxx+Pyy Where x, y are the two consumption goods whose prices are px and py, respectively. Her budget is B. a) From the first order conditions (FOCs) find expressions for the demand functions x* = x(px, Py, B) and y* = y(Px, Py, B) = b) Find an expression for the indirect utility function U* au* U(Px, Py, B). Verify that λ* = ав The consumer's utility maximization problem could be recast as the following Minimize pxx+Pyy s.t. U* = x(y + 1) c) Find the values of x and y that solve this minimization problem from FOCS d) Now suppose the SOCs are automatically satisfied so you do NOT have to check them. Derive the expenditure function E* = E(Px, py, U*) and show that the values of x and y that solve this minimization problem are equal to the partial derivative of the expenditure JE* JE* function, i.e. and respectively. apx apy

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Answer a From the first order conditions FOCs find expressions for the demand functions xpxpyI and y... View the full answer