4. Consider the following two-good utility function: u(x1, x2) xi+ Vx2. Answer the questions set out below. 'Tip: Go back to the definition of monotonic transformations on page 17 (theorem 1.2) to...

Extracted text: 4. Consider the following two-good utility function: u(x1, x2) xi+ Vx2. Answer the questions set out below. 'Tip: Go back to the definition of monotonic transformations on page 17 (theorem 1.2) to confirm that the transformation is effected by a strictly increasing function, in other words if v(x, u) = f(u(x, y)), ƒ is a strictly increasing function on the set of values taken on by u. 1 (a) What information is contained in the marginal rate of substitution of a utility function (apart from the fact that it represents the slope of the indifference curves)? Derive the marginal rate of substitution for the utility function u(x1, x2) above. (b) Explain why Hicksian demand functions are often referred to as "compensated demand functions". (c) If the corresponding budget constraint is given by y = P1x1 + P2x2, show that the con- sumer's Hicksian demand functions are x† (p, u) = („)´u² and x (p, u) = „) u? P2 pi+p2, Pi+p2 respectively. (d) What is the degree of homogeneity in prices of the Hicksian demand functions in (c) above? Provide an economic interpretation for this.