Production Finns Comparative Static The analysis so far can be used to show what happens when various prices change. The slope of the isoprofit line is w/p and so is affected whenever wl or p change y In the first graph, wi increases to wi and the result is a fall in the factor demand for input I and a fall in y In the second graph, p increases to p and the result is a rise in the demand for input I and a rise in the output y Changing w has no effect upon the slope and so nothing changes in the short run- except profit levels. iction -Frans Long Run Profit Maximisation In the long run all factors are variable. The firm solves the following problem m(1)一m吗→pMBG动=pB动=吗 Given the optimal amount of input 2(r?) the function pAP(r1, r?)=w'i defines the inverse factor demand cu which is the relationship between optimal factor demand and factor price, derived from the previous slide pMA(r1,r:) The factor demand alays downward sloping. There are no"Giffen"production inputs. Why not? A profit maximising firm with constant returns to scale makes zero profit. Why?Production — Firms 5 Comparative Statics • The analysis so far can be used to show what happens when various prices change. The slope of the isoprofit line is w1/p and so is affected whenever w1 or p change. . ................................................................................................................. . ................................................................................................................. ........................................................................................................................................................................................................................................................................................................... ........................................................................................................................................................................................................................................................................................... ............................ .................................................................................................................. .................................................................................................................. ........................................................................................................................................................................................................................................................................................................... ........................................................................................................................................................................................................................................................................................... ............................ 0 y x1 0 y x1 y = f(x1, x2) y = f(x1, x2) • x1 y • x 0 1 y 0 • • x1 y x 0 1 y 0 w1 p 0 w 0 1 p . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . • In the first graph, w1 increases to w 0 1 and the result is a fall in the factor demand for input 1 and a fall in y. • In the second graph, p increases to p 0 and the result is a rise in the demand for input 1 and a rise in the output y. • Changing w2 has no effect upon the slope and so nothing changes in the short run — except profit levels. Production — Firms 6 Long Run Profit Maximisation • In the long run all factors are variable. The firm solves the following problem: max x1,x2 pf(x1, x2) − w1x1 − w2x2 =⇒ pMP1(x ∗ 1 , x ∗ 2 ) = w1 and pMP1(x ∗ 1 , x ∗ 2 ) = w2 • Given the optimal amount of input 2 (x ∗ 2 ) the function pMP1(x1, x ∗ 2 ) = w1 defines the inverse factor demand curve which is the relationship between optimal factor demand and factor price, derived from the previous slide. ................................................................................................................................................................................................................................................................................ . pMP1(x1, x ∗ 2 ) = w1 0 w1 x1 • The factor demand curve is always downward sloping. There are no “Giffen” production inputs. Why not? • A profit maximising firm with constant returns to scale makes zero profit. Why?