Production Finns The Long and Short Run All factors can be varied in the long run. At least one is fixed in the short ru Suppose input 2 is land, and can only be varied in the long run. The short run production function is written f(r1, I2). It looks identical to the earlier function- getting fatter as I increases. Why? When all inputs are increased by a common factor k what happens to production? Returns to scale can be: 1.Constant: Output also increases by a factor of k-f(krl, kr2)= kf(r1, r2) 2. Decreasing: Output increases by less f(kI1, kr2)< kf(r1I2). 3. Increasing: Output increases by more than k-f(kr1, kr2)>kf(r1, I2) iction -Frans Short run profit maximisation Profit is total revenue minns total cost. If I z is fixed at I, in the short run and the prices of output and the two uts are given by p, wn and wz respectively, then short run profit is: x=py-wnr1-u2I2. Isoprofit lines are drawn by rearranging to give y as a function of I1. Hence y=(+u2E2)/p+(w/p)r Isoprofit lines =f(x1,z2) (丌+m22)/ lise profits. Pushing the isoprofit lines upward increases profit. However, they ca go higher than the production set as that output combination would be infeasible. Hence: pf(x1,x2)-11-m22= The slope of the isoprofit line is equal to the slope of the production function. This means the value of the marginal product is set equal to the price of the input. pMP(z, I2)=wn-a natural condition. WhyProduction — Firms 3 The Long and Short Run • All factors can be varied in the long run. At least one is fixed in the short run. • Suppose input 2 is land, and can only be varied in the long run. The short run production function is written y = f(x1, x2). It looks identical to the earlier function — getting flatter as x1 increases. Why? • When all inputs are increased by a common factor k what happens to production? Returns to scale can be: 1. Constant: Output also increases by a factor of k — f(kx1, kx2) = kf(x1, x2). 2. Decreasing: Output increases by less than k — f(kx1, kx2) < kf(x1, x2). 3. Increasing: Output increases by more than k — f(kx1, kx2) > kf(x1, x2). Production — Firms 4 Short Run Profit Maximisation • Profit is total revenue minus total cost. If x2 is fixed at x2 in the short run and the prices of output and the two inputs are given by p, w1 and w2 respectively, then short run profit is: π = py − w1x1 − w2x2. • Isoprofit lines are drawn by rearranging to give y as a function of x1. Hence y = (π + w2x2)/p + (w1/p)x1. . ................................................................................................................ ........................................................................................................................................................................................................................................................................................................... ........................................................................................................................................................................................................................................................................................... ........................................................................................................................................................................................................................................................................................... ........................................................................................................................................................................................................................................................................................... ............................ 0 y x1 y = f(x1, x2) Isoprofit lines (π + w2x2)/p • x ∗ 1 y ∗ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . • The firm is assumed to maximise profits. Pushing the isoprofit lines upward increases profit. However, they cannot go higher than the production set as that output combination would be infeasible. Hence; max π = max x1 pf(x1, x2) − w1x1 − w2x2 =⇒ w1 p = MP1(x ∗ 1 , x2) • The slope of the isoprofit line is equal to the slope of the production function. This means the value of the marginal product is set equal to the price of the input. pMP1(x ∗ 1 , x2) = w1 — a natural condition. Why?