The Marshallian demand function for good x is given by: x = I/(2px). The compensated demand function for good x is given by: xc = [(py/px)U]1/2. The indirect utility function for this consumer choice problem is given by: V(px, py, I) = I2/4pxpy. In this example, the substitution effect for good x own-price change (as opposed to cross-price effect) is given by the following equation: –a(I/px2), where a is a constant. What is the constant a? Please show steps.

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The Marshallian demand function for good x is given by: x = I/(2p_x). The compensated demand function for good x is given by: x^c = [(p_y/p_x)U]^1/2. The indirect utility function for this consumer choice problem is given by: V(p_x, p_y, I) = I²/4p_xp_y. In this example, the substitution effect for good x own-price change (as opposed to cross-price effect) is given by the following equation: –a(I/p_x²), where a is a constant. What is the constant a? Please show steps.