Economic Management #3: Production Theory and Costs

[samvara]

Before the seminar I went to a talk called Emerging Directors by Alison Gaines who is a Global Practice Leader on Board Consulting with Gerard Daniels. Heh. That's a mouthful. She talked about being a non executive director as a career, what they get paid, what they do and how they get their jobs.

Women on Boards is an Australian organisation looking to improve gender diversity on Boards - I've subscribed because I'm curious to see what kind of jobs are out there - although I'm probably not old/experienced enough to seriously consider these kinds of jobs yet.

It looks like Australian Boards are radically different to US ones, they call for -maybe- monthly meetings depending on level of involvement and have very little to do with day to day operations. I say this based on my (limited) experience of the OTW Board which meets frequently and has all members heavily involved in operations - being a non profit and volunteer organisation are factors here as well.

Bolted in to Economic Management 5 minutes late from the Boards talk in time to catch a quick round up on Point Income Elasticity and Cross Price Elasticities which looks like a cross between algebra and differential calculus. Yay!

Point Income Elasticity Problem
Suppose the demand function us: Q = 10 - 2P + 3Y; find the income and price elasticities at a price of P = 2, and income Y = 10

• Q = 10 -2( 2) + 3(10) = 36
• Income: E_Y = (change in Q / change in Y)(Y/Q) = 3(10/36) = 0.833
• Demand: E_D = (change in Q / change in P)(P/Q) = -2(2/36) = -0.111

Cross Price Elasticities
E_X = %Q_A / %P_B = change in QA / change in P_B)(P_B/Q_A)

• Substitutes have positive cross price elasticities: butter and margarine, or breakfast cereals
• Complements have negative cross price elasticities: golf round fees and demand for golf balls and gloves.

Tax Impacts: wikipedia has some good diagrams and explanations in pretty simple language *loves*

• tax burden depends on relative sopes of demand and supply curves
• with elastic demand and inelastic supply, producer pays larger portion of tax
• if supply is vertical (completely inelastic), producer pays all the tax
• if supply is horizontal (completely elastic), consumer pays all the tax

The Production Function: defines the maximum quantity of output that can be produced from a given amount of inputs.
Calculation: Q = f(K, L) ... Quantity of production (Q) = function of (F) (Capital (K), Labour (L))

e.g. I have bakers, I have ovens, how best to arrive at maximum production capacity?

Assume that labour is variable and easy to change - hire/fire people! This is a Short Run assumption, for Long Run scenarios we can change the scale of the entire operation

Measuring Productivity: to make effective input choices we need to have measures of input productivity
Calculation:

• Average Product = Q / L (how much we can produce per worker)
• Marginal Product = change in Q / change in L (how much each new worker produces)

There is a tendency to throw people at a problem until it goes away, what we find is that there is an optimum number of people after which the extra people aren't really helping much. Marginal Product is good at detecting this.

Labour Employed	Total Product (Output)	Marginal Product (MPL)	Average Product (APL)
0	0	...	...
1	2	2	2
2	5	3	2.5
3	9	4	3
4	12	3	3
5	14	2	2.8
6	15	1	2.5
7	15	0	2.1
8	14	-1	1.8

Analysis: Marginal Product (MP_L) tells us 3 workers are optimal, Average Product (AP_L) says 3 or 4 workers are optimal and that 5 workers is only a bit less optimal :p

• (MP_L) > (AP_L) - new employees will be more productive than existing average employees
• (MP_L) = (AP_L) - new employees will be less productive than existing average employees
• (MP_L) < (AP_L) - new employees will be less productive than existing average employees

Of course you can also re-evaluate your hardware (buy more ovens), fire your management team (or improve them) or do any number of other organisational type things.

The internet has provided this very pretty graph which is pretty enough to include. I believe MP_L = MPP and AP_L = APP in this scenario.



This is called the Law of Diminishing Returns.

Long Run Changes in Production

Some maths in a handy table - note that you can get a lot of output by either throwing in more Capital or more Labour or both - if you have enough money in your budget to do this kind of RECKLESS SPENDING.

Units of Capital (K)	Output	Output	Output	Output	Output	Output	Output	Output
8	37	60	83	96	107	117	127	128
7	42	64	78	90	101	110	119	120
6	37	52	64	73	82	90	97	104
5	31	47	58	67	75	82	89	95
4	24	39	52	60	67	73	79	85
3	17	29	41	52	58	64	69	73
2	8	18	29	39	47	52	56	52
1	4	8	14	20	24	24	21	17
Units of Labour (L)	1	2	3	4	5	6	7	8

Analysis: Observe the same numbers turn up for different combinations. These graceful curves are called isoquants and have the lovely quality of being more or less expensive than each other to implement - is Labour cheaper than Capital? This is called substituting.

Degrees of Substitution: the measure of the Marginal Rate of Technical Substitution (MRTS)
Calculation: MRTS = change in L / change in K

• Perfect Substitution: can add one person or one device for same output
• Imperfect Substitution: can add some people or some devices - relationship varies
• Perfect Complementarity: have fixed relationship (e.g. one driver per truck)

I confess writing this up I got horribly distracted by an case study on The Commando Hunt V which does a cost/benefit analysis (complete with isoquant-isocost chart (Fig 4.) comparing the cost of gunship team sorties to fighter-attack sorties. I also find I have a scribbled message to myself in the margin of my lecture notes saying 'find a good worked example. This is a good worked example :)

The optimal combination of inputs is based on the objective of minimising productions costs for a given output. Isocost lines are the combination of inputs for a given cost. Think of this as a production budget constraint.

Equimarginal Principle: Produce where MPL/CL = MPK/CK; i.e where marginal products per dollar are equal. If not, then either Labour (L) or Capital (K) are contributing more.

Allocative Efficiency

• is firm using the least cost combination of inputs?
• does it satisfy MPL/CL = MPK/CK

Technical Efficiency:

• is firm maximising potential output from a given set of inputs?
• firm should be on highest isoquant possible

Accounting Costs are usually based on historical costs
Economic costs are cased on cost data for making decisions and have a strong connection to management accounting but the focus is on opportunity cost.
Key decision making cost concepts

• Incremental Cost - extra cost of implementing a decision
• Marginal Cost - cost of last unit produced

...then we had a workshop and talked a lot about supply and demand curves ...oh gods my brain...

Comments

Board involvement in operations

[rabbit1080]

It looks like Australian Boards are radically different to US ones, they call for -maybe- monthly meetings depending on level of involvement and have very little to do with day to day operations. I say this based on my (limited) experience of the OTW Board which meets frequently and has all members heavily involved in operations - being a non profit and volunteer organisation are factors here as well.

Huh, I'd assumed that the OTW board situation was entirely because it's one of the classic things that happens in a non-profit organisation. I hadn't considered the possibility that there were also differences in how Boards operate in Australia and the USA. Am curious now :)

[maharetr]

Huh. This isn't a comment on the post itself, more surprise that it's dated 5th of June, and has turned up in a stack of circle posts all otherwise dated the 25th. Could it be something to do with the importer?

Re: Board involvement in operations

[samvara]

So am I! It's probably as you say, but Alison said there were big differences culturally as well.

[samvara]

Oh I date them so they appear chronologically where the class fell but let them appear on reading-view when I post them.