Consider two consumers, one whose preferences are Leontief and given by the utility function u = min{1, x}, and another whose preferences are Cobb-Douglas and given by the utility u = x^2. Their demands are given by the equations:
m1 = (p1 + p2)/(p1 + p2)
m2 = 2p2/p1
respectively. For each consumer, calculate the price elasticities 11, 12, 21, and 22, and income elasticities n1 and n2 as functions of P1, P2, and m.
Leontief:
Elasticity 11 =
Elasticity 12 =
Elasticity 21 =
Elasticity 22 =
Income elasticity n1 =
Income elasticity n2 =
Cobb-Douglas:
Elasticity 11 =
Elasticity 12 =
Elasticity 21 =