Graph and explain what the effects would be (short run production function) if a new advanced process was discovered

Firms use workers and capital to produce output. Workers are hired until profit is maximized which occurs when the marginal productivity of the last worker hired is equal to their real wage. Firms will keep substituting the cheaper input until costs are at the minimum which means profit is maximized. Thus profits are maximized when the extra cost of producing an added unit of output using labor is equal to the extra cost of producing an added unit of output using capital.

The shape of the firm's short term cost function can be graphed as price versus output. When this is done, the average total average cost curve intersects the marginal cost curve at the point where average cost is lowest. Firms maximize profit by producing at this output level, because it cannot dictate prices.

The short run production function is S-shaped when graphed on a plot of output vs. the variable input. As increasing amounts of the variable product are applied, eventually a point is reached where additional inputs actually decrease the output (think of having so many workers that they are tripping over each other). The new process will change the point where the S-curve bends because it will increase labor productivity. Fewer workers are needed to reach the point where additional inputs have no effect on output. Because labor productivity has increased, the firm will need fewer of them to maximize profits.