Week 7 - Applications of gradient vectors, Edgeworth box

Question 1

Formula for tangent lines/planes/hyperplanes (all the same)

Answer 1

(x - p) dot ∇f(p) = 0

where ∇f(p) is the gradient vector

Question 2

Tangency formula for Optimal bundle

Answer 2

∇u = λ(p1 p2…)

Note: write (p1 p2…) vertically

Question 3

3-step approach to finding the Contract curve

Answer 3

1. Calculate the MODIFIED utility for one of the functions
2. ∇u_A = λ ∇v_B <– gradient vectors
3. Rearrange in terms of λ, substitute and write out the equation of the contract curve!