Utiliy funcitons \( u(x,y) \) \( = min ( x, 2y ) \)
Consumer Equilibrium \( MRS(x,y) \) \( = \frac{p_x}{p_y} \)
Monopoly \( MR \) \(=MC \)
Perfect competition \( P \) \(=MC \)
Bertrand Competition \( p_1 \) \(=2p_2-5 \)
Cournot Competition \( q_1 \) \(=2q_2-5 \)
\( u(x,y) \) \( = min ( x, 2y ) \) 
\( MR \) \(=MC \)