- When to bind in european sword & buckelr?
- What sort of white rock with lots of small holes is this?
- How to represent dimension-$(0,n)$ matrices
- Issue plotting wormhole
- How to recover from this kind of startup error without reinstalling Mathematica?
- Odds on winning both hands running it twice when massive dog
- E. Coli metabolization of paracetamol
- Immune system vs pathogens
- What mutations in the DNA replication machinery would decrease the length of Okazaki fragments?
- Does the cell have a mechanism to determine DNA sequence from protein?
- How to search NCBI in bulk for a list of accession numbers?
- What is the grammar behind "上去“ in 听上去不错?
- What happened to the other dog?
- Relating two arrays
- Conservation law and hyperbolic conservation law
- What are the dimensions of a technic axle?
- Was Abu Simbel also designed to serve as a border between Egypt and Nubia?
- Did the Greek Theater in Taormina, Sicily also serve a strategic purpose?
- Is there an generally positive / appraisal / emotion boundary?
- Difference between forms of the georgian verbs with and/or without objective version vowel

# Solving additively separable preference with Lagrange

Suppose that the preferences of a consumer are additively separable in goods 1 and 2, i.e., her utility function is of the form u(x1,x2) = v1(x1) + v2(x2), where v''i(·) < 0 for i = 1,2. The prices of the two goods are p1 and p2, and the exogenous income is m.

(a) Formulate the Lagrangian for this consumer’s constrained utility-maximisation problem. Make sure you indicate the three decision variables. Find the three ﬁrst-order necessary conditions. Denote the decisions variables that solve this system as x1*(p1,p2,m), x2*(p1,p2,m), and λ∗(p1,p2,m).

(b)Substitute the optimal solutions from part (a) into the three ﬁrst-order necessary conditions. Then, partially diﬀerentiate each of the three ﬁrst-order necessary conditions with respect to m. Solve for ∂x1*/ ∂m and ∂x2*/∂m using Cramer’s Rule. Are both goods normal?

I understand getting

v1’(x1)-λp1=0

v2’(x2)-λp2=0

p1x1+p2x2=m

as your 3 first order equations but really can't see where you are supposed to