Consider a consumer with utility function u(x1, x2) = a_1x_1^( 2) + a_2x_2^( 2) where a1 > 0 and a2 > 0. Assume that p1, p2 > 0. (a) Show that the utility function represents strongly monotone preferences (b) Draw indifference curves passing through points (1, 2), (3, 3) and (0, 3). What properties of the preference relation can you derive from these indifference curves? (c) State the expenditure minimization problem and derive the Hicksian demand. Does the EMP problem have a unique solution at every price vector p >> 0? (d) Derive expenditure function e(p, u). Verify that it is homogeneous of degree 1 in p and increasing in u. (e) Using expenditure function and Hicksian demand, calculate Walrasian demand and indirect utility
Consider a consumer with utility function u(x1, x2) = a_1x_1^( 2) + a_2x_2^( 2) where a1 > 0 and a2 > 0. Assume that p1, p2 > 0. (a) Show that the utility function represents strongly monotone preferences (b) Draw indifference curves passing through points (1, 2), (3, 3) and (0, 3). What properties of the preference relation can you derive from these indifference curves? (c) State the expenditure minimization problem and derive the Hicksian demand. Does the EMP problem have a unique solution at every price vector p >> 0? (d) Derive expenditure function e(p, u). Verify that it is homogeneous of degree 1 in p and increasing in u. (e) Using expenditure function and Hicksian demand, calculate Walrasian demand and indirect utility
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Consider a consumer with utility function u(x1, x2) = a 1x_1^( 2) + a_2x_2^( 2) where a1 > 0 and a2 > 0.
Assume that p1, p2 > 0. (a) Show that the utility function represents strongly monotone preferences (b)
Draw indifference curves passing through points (1, 2), (3, 3) and (0, 3). What properties of the
preference relation can you derive from these indifference curves? (c) State the expenditure
minimization problem and derive the Hicksian demand. Does the EMP problem have a unique solution
at every price vector p >> 0? (d) Derive expenditure function e(p, u). Verify that it is homogeneous of
degree 1 in p and increasing in u. (e) Using expenditure function and Hicksian demand, calculate
Walrasian demand and indirect utility
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