1
vote
0answers
30 views

Prove that the partial derivatives of $(y-g_i+a\sum^n_{j=1} g_j)$ are positive

I have a function: $$\pi_i^1=y-g_i+a\sum^n_{j=1}g_j,$$ where 0 < a<1< na, and I need to prove this: $$\frac{\partial(\sum^n_{i=1}\pi^1_i)}{\partial g_i}=-1+na>0.$$ I am not very ...
0
votes
3answers
124 views

How to write “the parameter maximizing the maximum of the maximum value of two functions continuous in the domain of maximization”

Say you have $f(x),g(x)$ continuous where they need to be and you want to express the following: Give me the biggest value of $f$ for $x \leq X_f$ , give me the biggest value of $g$ for $x \leq X_g$, ...
0
votes
1answer
2k views

cournot equilibrium and stackelberg equilibrium question

Question is as follow: there are 2 firms that want to enter the apple juice market in country A. There are no existing firms in the market or potential entrants. They need to decide on yearly ...
4
votes
1answer
230 views

Meaning of a partial derivative here?

I am given a 'tariff' function for two countries, $i=1, 2$. Both players can select a tariff between 0 and 100. If player $i$ selects $x_i$ and player $j$ selects $x_j$, country $i$ gets a payoff of ...
5
votes
1answer
445 views

Finding Nash equilibrium aka finding where lines intersect

I am tagging this as multivariable calculus because it potentially involves taking partial derivatives. I am working on some mathematical treatment for Cournot duopoly models (not homework, just ...