Unformatted text preview: Profit Maximization 120 Profit Maximization A. Profits defined to be revenues minus costs 1. value each output and input at its market price --even if it is not sold on a market. 2. it could be sold, so using it in production rather than somewhere else is an opportunity cost. 3. measure in terms of flows. In general, maximize present value of flow of profits. B. Stock market value 1. in world of certainty, stock market value equals present value of stream of profits 2. so maximizing stock market value is the same as maximizing present value of profits 3. uncertainty --- more complicated, but still works C. Short-run and long-run maximization 1. fixed factors --- plant and equipment 2. quasi-fixed factors --- can be eliminated if operate at zero output (advertising, lights, heat, etc.) Profit Maximization 121 OUTPUT Isoprofit lines slope = w 1 /p y* w2 x 2 p + p y = f (x 1 , x 2 ) production function x1 * x1 Figure 18.1 D. Short-run profit maximization. Figure 18.1. 1. max pf (x) wx 2. pf 0 (x ) w = 0 3. in words: the value of the marginal product equals wage rate 4. comparative statics: change w and p and see how x and f (x) respond E. Long-run profit maximization 1. p @[email protected] = w1 , p @[email protected] = w2 Profit Maximization 122 F. Profit maximization and returns to scale 1. constant returns to scale implies profits are zero a) note that this doesn't mean that economic factors aren't all appropriately rewarded b) use examples 2. increasing returns to scale implies competitive model doesn't make sense G. revealed profitability 1. simple, rigorous way to do comparative statics 2. observe two choices, at time t and time s 3. (pt ; wt ; y t ; xt ) and (ps ; ws ; y s ; xs ) 4. if firm is profit maximizing, then must have pt yt wt xt pt ys wt xs ps ys ws xs ps yt ws xt
5. write these equations as pt yt wt xt pt ys wt xs ps yt + ws xt ps ys + ws xs Profit Maximization 123 6. add these two inequalities: (pt ps )yt (wt ws )xt (pt ps )ys (wt ws )xs
7. rearrange: (pt ps )(yt ys ) (wt ws )(xt xs ) 0
8. or py wx 0 9. implications for changing output and factor prices ...
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This note was uploaded on 06/16/2008 for the course ECON 201 taught by Professor Johnson during the Spring '08 term at Aarhus Universitet.
- Spring '08