The supply function Sj(p), may not be well-defined when assumption P.4 is not satisfied and firm j's technology set, Yj, is unbounded. Consider the production technology in R2: Yj={(x,y)R2x0,y2x+x}. Recall that inputs are treated as negative co-ordinates and outputs are treated as positive, making this all a bit obscure (If we were writing a production function and x were measured positively instead of negatively, we would have y=2x+x ). A. Demonstrate that Yj is unbounded, violating P.4. B. Show that for some prices, for example (px,py)=(7,7); that Sj(p) is not welldefined, i.e., there is no profit maximizing bundle. The supply function Sj(p), may not be well-defined when assumption P.4 is not satisfied and firm j's technology set, Yj, is unbounded. Consider the production technology in R2: Yj={(x,y)R2x0,y2x+x}. Recall that inputs are treated as negative co-ordinates and outputs are treated as positive, making this all a bit obscure (If we were writing a production function and x were measured positively instead of negatively, we would have y=2x+x ). A. Demonstrate that Yj is unbounded, violating P.4. B. Show that for some prices, for example (px,py)=(7,7); that Sj(p) is not welldefined, i.e., there is no profit maximizing bundle