chapter 12h - behind the supply curve - inputs and costs

8/13/2019 Chapter 12H - Behind the Supply Curve - Inputs and Costs

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Econ 101: Principles of Microeconomics

Chapter 12 - Behind the Supply Curve - Inputs and Costs

Fall2010

Herriges (ISU) Ch. 12 Behind the Supply Curve Fall 2010 1 / 30

Outline

1 The Production Function

2 Marginal Cost and Average Cost

3 Short-Run versus Long-Run Costs



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Overview

In this chapter we turn our attention to the firm.

Afirmis an organization that produces goods or services for sale.

We will begin by characterizing the relationship between the firmsinputs and the quantity of outputs it produces.

Theproduction functiondescribes the relationship between thequantity of inputs and the quantity of outputs that the firm produces.

Basic characteristics of the production function has implications forthe cost structure for the firm, which in turn has implications for thefirm ultimate supply function.


The Production Function

The Short Run and the Long Run

It is useful to categorize firms decisions into

- Long-run decisionsinvolves a time horizon long enough for a firm tovary all of its inputs

- Short-run decisionsinvolves any time horizon over which at least oneof the firms inputs cannot be varied

To guide the firm over the next several years, manager must use thelong-run view

To determine what the firm should do next week, the short run viewis best.



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Production in the Short Run

In the short-run, the firms inputs can be divided into one of twocategories

1 Fixed inputs

- These are inputs whose quantity is constant for some period of time

(regardless of how much output is produced).- Typically, fixed inputs will include land and machinery, though they can

also include certain types of labor (due to contracts).

2 Variable inputs

- These are inputs whose quantity the firm can vary, even in the shortrun.

- Examples of variable inputs often include labor, energy, fuel, etc.

When firms make short-run decisions, there is nothing they can doabout their fixed inputs; i.e., they are stuck with whatever quantity

they have.However, they can make choices about their variable inputs.



Total Product

To fix ideas, suppose we have a firm whose only variable input is labor

All other inputs (capital, land, raw materials, etc.) we will assume fornow are fixed.

Total productis the maximum quantity of output that can beproduced from a given combination of inputs.

Thetotal product curveshows how the quantity of output depends onthe quantity of variable input, for a given quantity of the fixed input.

We would generally expect the total product curve to be increasing;i.e., as the quantity of the variable input increases, we would expecttotal output to increase.



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Consider Johns Woodworking Shop Again

Units of Labor Total Product0 01 102 353 804 1605 1936 2187 2398 257



The Total Product Curve



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Marginal Product

Notice that the Total Product curve is always increasing in this case,but that its slope is not the same throughout.

- Initial the slope is increasing- but eventually it starts to flatten out.

The slope of the Total Product Curve is theMarginal Productoflabor.

Formally,

Marginal Product of Labor (MPL) = Change in Quantity of Output

Change in Quantity of Labor

= Q

L

Tells us the rise in output produced when one more worker is hired



Units of Labor Total Product Marginal Product0 010

1 1025

2 3545

3 8080

4 160

335 193

256 218

217 239

188 257



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The Marginal Product Curve



Marginal Returns To Labor

As more and more workers are hired, the MPL is at first increasing

- This is known asincreasing returns to labor- This is typically due to the returns to specialization- It can also arise due to minimum labor requirements for equipment.

Eventually, however, the MPL starts to decline

- This is known asdiminishing returns to labor

- This arises as the gains from specialization are exhausted and- The constraints caused by the fixed inputs start to bind

This pattern of MPL (and for other inputs) is thought to hold formost industries.

Consider the problem of a woodworking shop.



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Marginal Cost and Average Cost

Production and Firm Costs

Understanding the nature of a firms production function is importantin that it has implications for the firms costs.

In the short run, the firms costs can be divided into two broadcategories:

1 Total Fixed costs (TFC): These are costs that do not depend upon thequantity of output produced.

- These costs are typically associated with fixed inputs.- Examples of fixed costs might be the rent paid for the firms building or

equipment rentals.

2 Total Variable costs (TVC): These are costs that depend on thequantity output produced.

- As the name suggests, these are costs associated with the variableinputs.

- In the case of Johns Woodworking shop, theTVC

=w L

wherew

denotes the wage rate.

Total Costs= TFC + TVC.



Johns Cost Structure

Suppose that John has a TFC of 5000 and pays a wage rate of

1200 per week

Units of Total Total Fixed Total Variable TotalLabor Output Cost (TFC) Costs (TVC) Costs (TC)

0 0 5000 0 50001 10 5000 1200 6200

2 35

5000

2400

74003 80 5000 3600 86004 160 5000 4800 98005 193 5000 6000 110006 218 5000 7200 122007 239 5000 8400 134008 257 5000 9600 14600



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The Cost Curves



Marginal and Average Cost Curves

While the breakdown of Total Cost into Total Fixed and TotalVariable Costs is helpful, two other measures of cost will be evenmore useful:

1 Marginal Cost: Measures the additionalcost of producing one moreunit of a good or service.

2 Average Cost: Measures the averagecost per unit of the good or

service (i.e., the costs averaged over allof the output produced by thefirm).

Understanding the distinction between these two concepts will be keyto finding the optimal level of production for the firm.

Well start with average cost



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Average CostsThere are three types of average costs

1 Average Fixed Costs (AFC)= Total Fixed Costs divided by Output

AFC = TFC

Q (1)

Since the numerator is fixed, AFC will decline as output increases.2 Average Variable Costs (AVC)= Total Variable Costs divided by

Output

AVC = TVC

Q (2)

- Since TVC is initial slowing down as output increases (with increasingreturns to labor), AVC will initially fall as output increases.

- As TVC starts to increase more rapidly with output (with diminishing

returns to labor), AVC will start to increase with output.3 Average Total Costs (ATC)= Total Costs divided by Output

ATC = TC

Q =AFC+AVC (3)



Johns Average Costs

Units of Labor Total Product AFC AVC ATC1 10 500.00 120.00 620.002 35 142.86 68.57 211.433 80 62.50 45.00 107.504 160 31.25 30.00 61.25

5 193 25.91 31.09 56.996 218 22.94 33.03 55.967 239 20.92 35.15 56.078 257 19.46 37.35 56.81



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Adding in the MC Curve



Patterns in the MC and AC Curves

Notice that the MC curve is

- Initially declining- this is due to increasing returns to labor- Eventually increasing- this is due to diminishing returns to labor

Theminimum-cost output, Qmin, is the quantity at which the averagetotal cost is lowest.

- This is at the bottom of the ATC curve.- and occurs where ATC=MC

At outputs less than Qmin, ATC >MC and ATC is falling.

At outputs greater than Qmin, ATC < MC and ATC is rising.



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Short-Run versus Long-Run Costs

Production Costs in the Long Run

Up until now, we have been focussing on the short-run, with some ofthe firms inputs held fixed.

In the long run, costs behave differently

Firm can adjust all of its inputs in any way it wantsIn the long run, there are no fixed inputs or fixed costs; i.e. all inputsand all costs are variable

Firm must decide what combination of inputs to use in producing anylevel of output

The firms goal is to earn the highest possible profit

To do this, it must follow the least cost rule; i.e., to produce any givenlevel of output the firm will choose the input mix with the lowest cost

This yields aLong-Run Average Total Cost Curve; i.e., therelationship between the output and the ATC when fixed costs arechosen to minimize total cost for each level of output.



Consider Johns Woodworking Shop

Suppose that in our first production function, we assumed that Johnhad only one set of tools (e.g., 1 table saw, 1 drill press, and 1 routertable).

Well call this one unit of capital

The tools (and the space to house his tools) constitute fixed costs forJohn in the short-run.

In the long-run, John must decide whether or not he wants to expandhis capital stock

The trade-off is that additional capital will avoid worker congestion,but imposes a large fixed cost on the firm.

At low levels of production, having just one set of tools is not a bindingconstraint and John would rather avoid the additional capital costs.At higher levels of production, additional capital will avoid congestionproblems and the capital costs are spread out over more units ofproduction.



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Different Levels of Capital

Labor Units of CapitalUnits of Labor Capital = 1 Capital = 2 Capital = 3

0 0 0 01 10 10 102 35 39 393 80 92 1014 160 184 2025 193 284 3146 218 397 4397 239 443 5718 257 478 709



The Corresponding ATC Figures are Given by



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Johns Capital Stock ChoiceThe level of capital stock John chooses depends on his expected level ofoutput



If Capital Stock Can be Varied Continuously, We Get



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Returns to Scale

LRATC curves for industries usually exhibit three basic phases:1 Increasing Returns to Scale: Output range with declining LRATC

This is also known aseconomies of scaleEconomies of scale often arise due to the gains from specialization.The greatest opportunities for increased specialization occur when afirm is producing at a relatively low level of outputEconomies of scale can also arise due to minimum size requirements forcertain types of equipment.

2 Constant Returns to Scale: Output range with constant LRATC

Over some range of production, size may not matter and firms of thesame size will be equally cost-effective.

3 Decreasing Returns to Scale: Output range with increasing LRATC

This is also known asdiseconomies of scaleAs output continues to increase, most firms will reach a point where

bigness begins to cause problemsThis is true even in the long run, when the firm is free to increase itsplant size as well as its workforceDiseconomies of scale are more likely at higher output levels



chapter 12h - behind the supply curve - inputs and costs

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