An indifference curve is given by X0.4Y0.7 = 100, where X and Y are quantities of goods X and Y consumed, with Y is on the vertical axis and X is on the horizontal axis.
Find the slope of the indifference curve.
Does the marginal rate of substitution (MRS) diminish along the indifference curve when X increases? Prove your answer.
A generalized production function Q=f(K,L) is defined implicitly from the following equation, f(Q, K, L) = QerQ-AKaLb = 0. Find the marginal product of L and K, and the MRTS.
A demand function for good X is given by X=APx
PyβIγ, where A>0, Px and Py are prices of good X and the other good Y, I is the income, α, β, and γ are parameters. Find the own-price elasticity, cross-price elasticity, and income elasticity. Show your work. Discuss signs of α, β, and γ.
Given A=2 3 14 1 25 3 4 and B=2 7 05 8 16 7 0 .
a) Find AB and BA, showing AB
BA.
b) Show that det(AB) = det(BA) = (detA)*(detB).
c) Find A+B and show that det(A+B) det(A)+det(B).
