No Slide Titleeconweb.rutgers.edu/killings/Econ_102/Krug3e_Micro_CH11_part3.pdf · 2. Now for a...

Microeconomics Third Edition

Chapter 11 Behind the Supply Curve: Inputs and Costs

Copyright © 2013 by Worth Publishers

Paul Krugman and Robin Wells

Part 3: Conclusion

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”

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!

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.”

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 = TP10 and marginal product = MPL10

with K = 20, total product = TP20 and marginal product = MPL20

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

Figure 11.4 Total Cost Curve for George and Martha’s Farm

Krugman and Wells: Microeconomics, Third Edition Copyright © 2013 by Worth Publishers

Q1 = 84

VC1 = 1200

TC1 = 1400

FC = 400

Note: as Q rises,

• AVC always rises

• MC always rises

• AFC (= FC/Q) always falls

• ATC first falls, then rises

Minimum ATC occurs at QT

ATC is falling for Q < QT

ATC is rising for Q > QT

For Q < QT, ATC > MC

and ATC is falling

For Q > QT, ATC < MC

and ATC is rising

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)

Table 11.1 Costs at Selena’s Gourmet Salsas


Figure 11.6 Total Cost and Marginal Cost Curves for Selena’s Gourmet Salsas


Table 11.2 Average Costs for Selena’s Gourmet Salsas


Figure 11.7 Average Total Cost Curve for Selena’s Gourmet Salsas


Figure 11.8 Marginal Cost and Average Cost Curves for Selena’s Gourmet Salsas


Figure 11.9 The Relationship Between the Average Total Cost and the Marginal Cost Curves


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

Figure 11.10 More Realistic Cost Curves


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

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

Figure 11.12 Short-Run and Long-Run Average Total Cost Curves


Table 11.3 Concepts and Measures of Cost


No Slide Titleeconweb.rutgers.edu/killings/Econ_102/Krug3e_Micro_CH11_part3.pdf · 2. Now for a...

Documents

Transcript of No Slide Titleeconweb.rutgers.edu/killings/Econ_102/Krug3e_Micro_CH11_part3.pdf · 2. Now for a...