Microeconomics. Chapter 11 Behind the Supply Curve: Inputs and Costs. Third Edition. Part 3: Conclusion. Paul Krugman and Robin Wells

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2 2. Now for a slightly more complicated model, based on a slightly more complicated short-run production function the same definitions apply: e.g., when L = 4, average product of labor = APL = Q/L = 64/4 = 16 = slope of origin line (from origin to the relevant point on SRPF) marginal product of labor = MPL = ΔQ/ΔL = (75-64)/(5-4) = 11 = slope of tangent line

3 Note that this SRPF has diminishing marginal product or diminishing returns : as the level of labor input (and output) rises, the returns (gain in output) get smaller. (See previous slide!) Note also that diminishing does not mean negative It just means getting smaller!

4 If Q actually falls when we add L, we do have negative returns i.e., negative marginal product Examples: programmers working insane hours; rice farmers trampling the plants, etc. Again, note that this is NOT the same as diminishing returns.

5 Note that SRFP can be shifted up if there is more capital (K). This will therefore raise MPL. for example: with K = 10, total product = TP 10 and marginal product = MPL 10 with K = 20, total product = TP 20 and marginal product = MPL 20

6 Next: invert the short run production function ( TP curve ) to get the labor requirements function, showing L required to produce each level of Q. Then: multiply the labor requirements function by the wage, to get W L = variable cost schedule (VC): shows labor cost (= variable cost, WL) of producing each level of Q. Then: graph fixed costs FC at each level of output; add FC to VC at each level of output to get TC = FC + VC (again, note that TC schedule is just the VC schedule, shifted up by the amount of TC) Finally, get the average and marginal curves: at each level of output, ATC = TC/Q = slope of origin line from origin to TC curve AVC = VC /Q = slope of origin line from origin to VC curve AFC = FC/Q = slope of origin line from origin to FC curve MC = ΔTC/ΔQ = ΔVC/ΔQ = slope of line tangent to the TC curve

9 TC 1 = 1400 VC 1 = 1200 FC = 400 Q 1 = 84

10 Note: as Q rises, AVC always rises MC always rises AFC (= FC/Q) always falls ATC first falls, then rises Minimum ATC occurs at Q T ATC is falling for Q < Q T ATC is rising for Q > Q T For Q < Q T, ATC > MC and ATC is falling For Q > Q T, ATC < MC and ATC is rising

11 A general rule: whenever MC < ATC, ATC is falling whenever MC > ATC, ATC is rising whenever MC = ATC, ATC stays the same e.g., your cumulative average is like the ATC backward looking and your semester average is like the MC forward looking whenever your semester average is below your cumulative average, your cumulative average will fall; whenever your semester average is above your cumulative average, your cumulative average will rise (Or think of batting averages ) Note that MC is closely related to MPL: MC = ΔTC = Δ(FC + VC) = ΔVC = Δ(WL) = W ΔL = W = W ΔQ ΔQ ΔQ ΔQ ΔQ (ΔQ/ΔL) MPL so MC = marginal cost of additional output = W (cost of additional labor) divided by MPL (additional output generated by additional labor)

18 A slightly different S-shaped production function produces a slightly different set of cost curves: Note that here, MPL first rises and then falls: increasing marginal product at low levels of Q, then diminishing marginal product at higher levels of Q So here, MC = W/MPL will first fall as output rises, and will then rise as Q rises

20 3. Costs in the long run A. in the long run, all inputs can change (K as well as L) so in the long run, costs depend on economies or diseconomies of the entire scale of operations (including both K and L) B. economies/diseconomies of scale: increasing returns to scale: raise all inputs by x% output rises by more than x% constant returns to scale: raise all inputs by x% output also rises by x% decreasing returns to scale: raise all inputs by x% output rises by less than x% WARNING about sound-alikes that aren t alike! diminishing returns refers to change in MPL as amount of L used rises, with K constant decreasing returns to scale refers to change in output as all inputs are changed by same percentage

21 C. returns to scale and costs: if all inputs change by x%, then costs will change by x% as well raising all inputs by x% will raise costs by x%, so with increasing returns to scale: output rises by more than x%, costs rise by only x%, so TC/Q will fall with constant returns to scale: output rises by x%, costs rise by x%, so TC/Q will remain the same with decreasing returns to scale: output rises by less than x%, costs rise by x% so TC/Q will rise D. from the short run to the long run: the firm moves from one scale of operations to another picking a larger or smaller capital stock for the next short-run so the long-run cost curve is the outer envelope of the short-run cost curves, showing the size of plant that will produce each level of output at lowest cost

Technology, Production, and Costs

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