6 votes

Perfect substitutes and Lagrange

Your Lagrangian would be $$L = (ax+by)+\lambda (I−p_x x−p_y y) +\mu_x(x−0)+\mu_y(y-0),$$ where the final two terms represent the restriction that $x,y\geq0$. You then arrive at conditions $$\frac{\...
Bayesian's user avatar
  • 5,290
5 votes

Contradictory FOC and maximizing solution

As alluded to by Bertrand in his +1 comments this is because FOCs do not tell you where maximum or minimum occurs. This is common misconception among some students but it simply does not hold. FOCs ...
1muflon1's user avatar
  • 56.4k
5 votes

How to find the contract curve when both agents have linear utilities?

I rewrite the problem of maximization you wrote (I omit the endowments): $\max x_A + y_A \;\;\qquad (1)$ subject to $s x_B + y_B = \overline{U}\qquad (2)$. This problem can be seen as a problem of ...
BakerStreet's user avatar
  • 3,697
3 votes

How to find the contract curve for a funky utility involving the min operator?

Given a pure-exchange economy: $u_1(x_1,y_1) = \min(3x_1+y_1,x_1+3y_1)$, $u_2(x_2,y_2)= x_2^{0.5}y_2^{0.5}$ Total Endowments of X and Y are $\omega^X > 0$, and $\omega^Y > 0$, respectively. ...
Amit's user avatar
  • 8,476
2 votes

Example of a (not quasi-linear) production function whose inputs are not perfect substitutes but are not asymptotic at the axes

You could, for example take the function $f: \mathbb{R}^2_+ \times[0,1] \to \mathbb{R}$. $$ f(L,K, \rho) = L + K + (1-\rho) L K. $$ For $\rho = 1$, we have $f(L, K, 0) = L + K$ which is a production ...
tdm's user avatar
  • 12k
2 votes

Finding Walrasian equilibria when Walrasian demands are not unique

let us first write the demand functions of individual $A$ and $B$ $$(x_A^d,y_A^d)(p_x,p_y,m_A)\in\left\{\begin{matrix} (\frac{m_A}{p_x},0) & ,\frac{p_x}{p_y}<1\\ (0,\frac{m_A}{p_y}) & , \...
mynameparv's user avatar
1 vote

A utility function (neither perfect substitues nor perfect complements) which stems from a CES f. and leads to gross complements or gross substitutes

We can show if a utility function exhibits complementarity or substitutability just from its function, without having any information about prices. The utility function gives information about the ...
enthusiastic economist's user avatar

Only top scored, non community-wiki answers of a minimum length are eligible