Question

Derive the indirect utility function form the given direct utility function . , dddddP 0 d,. Use Roy’s identity to construct demand functions for the two goods dP and d,. Are these same as demand functions derived from the direct utility function?

Answer 1

Answer on Question # 72601, Economics / Microeconomics

$$U(Px, Py, M) = \max \left\{ U(x, y) \mid Px + Py = M \right\} = U(x^*, y^*) = U(Dx(Px, Py, M), Dy(Px, Py, M))$$

Roy's Identity: $x^* = \left( -\frac{\partial U^*}{\partial Px} \right) / \left( \frac{\partial U^*}{\partial M} \right)$

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