Question

3. Consider the following utility function, (a) 15 points] Derive the Marshallian demand functions. (Explain your derivation in details.) Does the Marshallian demand increase with price? Are the two consumption goods normal goods? (b) 15 points] Derive the Hicksian demand functions. Does the Hicksian demand ncrease with price

Answer 1

u = min [x^a_1, bx^a_2] (a) at optimal allocation x^a_1 = bx^a_2 x_1 = (b)^1/a x_2 budget constraint: P_1 X_1 + P_2 X_2 = I P_1 (b)^1/a x_2 + p_2 x_2 = I implies x^m_2 = I/P_1 b^1/a + p_2 x^m_1 = I (b)^1/a/P_1 b^1/a + p_2 partial differential x^m_2/ partial differential P_1 = -I (p_1 b^1/a + p_2)^-2 (b^1/a) as P_1 increase x^m_1 decreases both goods are normal (b) For demand u = x^a_1 = b x^a_2 x^H_1 = (u)^1/a, x^H_2 = (u/b)^1/a here demand functions are independent of price