Labour Demand and Productivity
LABOUR DEMAND AND PRODUCTIVITY
- Text: Benjamin, Gunderson, Lemieux and Riddell, Ch. 5, some of Ch. 6
(Quasi-fixed costs), parts of Ch. 13 (incentive pay)
Marginal Productivity Theory of Short-run Labour Demand:
- In short-run the following are givens:
- technology
- quantity of non-labour inputs
- firm organization
- Competitive labour market: many small employers, many workers.
- Simple idea:
- Employers seek to maximize profits.
- So, hire more labour if:
benefit > costs
Employer’s Benefit from hiring an extra unit of labour?
- The value of what that labour produces:
(Extra output from an extra unit of L)x (Extra money per unit of extra output)
= (marginal physical product of labour) x (marginal revenue)
= MPP x MR
= Marginal revenue product (MRP)
- The marginal revenue product curve plots the MRP against the quantity of
labour.
Shape of the MRP curve:
- Key question:How does MPP vary with L other things equal?
- other things?
quantity of other inputs
technology
firm organization and incentives .
- MPP curve: - may be upward sloping at low levels of L
- downward sloping at high L.
- Why?
- Low L: specialization, division of labour possibilities at low L.
MPP may rise initially as L rises.
(More L: less changeover time between tasks, better task
assignment, specialist becomes better at task, etc.)
- Higher L:
Diminishing returns: MPP eventually declines holding
other inputs constant.
Why?
- As L increases, each unit of L has less of the other inputs to
work with.
- Diminishing returns can give a downward sloping MRP curve.
- An additional consideration: How does MR vary with L?
- Key: the competitiveness of the output market.
- Competitive output market:
- Firms are too small to affect the price of their product.
- So: Marginal Revenue (MR) = Price of output (P).
- More L, more output, same price so MR is the same.
- Then shape of MRP driven by shape of MPP only.
- Non-competitive product market:
- The amount the firm produces affects the price it is paid.
- More output, must cut the price to sell it.
- Result: MR declines with output and L.
- MRP steeper downward slope than MPP.
Cost of an Extra Unit of Labour:
- Competitive labour market: employer must pay the “going rate” (W).
- Must pay as well as other, competing employers.
- small employer: wage independent of quantity hired (wage taker).
(labour supply to an individual employer is flat at W)
- Later: will consider a wage-setting employer ("monopsony").
- Other labour costs?
- if they vary directly with time-worked can be treated as part of W;
- if don’t vary directly with time-worked: fixed cost (see below).
Employer Hiring Decision:
- MRP curve: shows employer gain from hiring extra L.
- W is the cost of extra L.
- Hire more labour as long as: W<MRP
- Do not hire if:W>MRP
Result?
- Firm hires up to the point where
MRP=W
- At this point each unit of L is paid W.
- The wage the worker earns is tied to productivity.
i.e., labour is paid its marginal product.
- Role of competition and worker mobility?
- say a worker is underpaid (W<MRP)
- competing employer: profitable to pay a wage closer to MRP
- worker is bid away unless they are paid W=MRP.
Short-run Labour demand curve for the firm:
- Hire where W=MRP: this gives the quantity of labour demanded.
- Labour demand curve: downward sloping part of the MRP curve.
(More precisely downward sloping part where Average Revenue Product > MRP -- text Fig. 5.1)
- If at point where W=MRP on upward sloping part of MRP:
profits minimized! economically irrelevant.
- Short-run demand curve: holds technology, plant, machines, etc. fixed.
- Income distribution and this outcome? area under MRP is total value of output; WL is total wages paid; rest goes to other inputs or is profit.
Labour demand curve shifts:
- Can shift due to changes in MPP:
- Change in amount or quality of other factors of production
- Change in technology (process innovation)
- can raise productivity of existing jobs
- could lead to new ones too (MP=0 rises to >0)
- Change in organization or incentives.
- Can shift due to changes in MR
- Change in output price, position of the firm's product demand curve.
[ technology (product innovations) can work through MR ]
(see website: Varian's article on productivity, computers and organization in the U.S.)
Market Level Labour Demand Curve:
- Market demand curve: shows the quantity of labour demanded by all firms that
hire that type of labour.
- horizontal sum of labour demand curves over all employers (see text Fig.7.1)
- Possible complication? (pecuniary externality)
- As all employers change L, the price of their output couldchange.
(say ↑L → ↑Supply of output → ↓Price so ↓MR)
- This shifts firmlabour demand curves and gives a steeper marketlabour
demand curve (output price effect dampens change in L).
- In market equilibrium: W=MRP across all employers.
- Shifts in market demand occur for the same reasons as shifts in firm labour
demand.
- note: feedback through output price changes is possible if the shift
affects many employers.
- at the industry level feedbacks through the output price are often important.
- rising physical productivity may translate into low prices, not higher
labour demand and higher wages.
i.e. MP rises, MR falls so MRP is almost unchanged.
Applications and Implications of MP Theory: Productivity and Wages
- Marginal productivity theory links wages and productivity (MRP).
- Historical wages trend and productivity.
- They tend to move together over the long-term (consistent with MP
theory)
- An important prediction:
- contrast this to many Marxist-radical economist predictions.
i.e., exploitation, employer reaps gains.
- MP theory provides a partial explanation of differences in wages between
jobs, workers, countries, etc.
- look to determinants of productivity to explain wages
- Skill level:
- determines what kinds of tasks the worker can do. Can they produce high MRP goods and services?
(education and training affect skills and a person's MRP)
- Quantity and quality of non-labour inputs.
- Business investment, government investments in
infrastructure can affect MRP.
(Krueger article: computers, pay and productivity)
- Technology
- affects productivity and via competition pay.
- Industrial Revolution: low-skill winners (higher MRP).
- Organization
- Henry Ford’s assembly line
- Schmitz paper (website): “What determines productivity?”
- role of work-rules in contracts of Minnesota / N. Ont. iron
industries in 1980s.
- Health and nutrition: can affect MRP in a given job type (this and low
wages in less developed countries)
- Think about average wage in India vs. Canada in terms of the above factors.
- MP theory is a partial explanation of wages? Supply matters too.
Sky-high wages: Can the model explain them?
- See text: Chapter 13 “Economics of superstars” pp. 375-376, “Tournaments”
pp.376-378, “Executive Compensation” pp. 386-387.
- Sports star "Joe Hero" paid $8 million per year.
- Star actress "Jill Fame" paid $5 million for a movie.
- CEOs, finance whizzes, corporate lawyers paid millions.
- Can such high wages be explained by marginal productivity theory?
- MP theory: Joe’s high wage reflects his value to the team owners:
- extra attendance revenues, sale of team products, TV rights, etc.
- competition between teams ensures that Joe is paid his worth
- similar stories for the others: high pay reflects a combination of high
value and competition.
- Economics of Superstars and Winner-Take-All Markets:
- Concern with cases where the best are paid massively more than the
next best.
- This can occur even if the “best” is only slightly better than the next best.
i.e. small differences in skill are magnified into large
differences in value and pay.
- Why? Rooted in the nature of the service being provided.
- actor, author, athlete: large audience with a taste for the best.
- manager of a large organization: can improve the productivity of
a large number of people serving a large market.
- tasks where the ‘winner’ gets all the gains (e.g. top lawyers)
- Incentive models of compensation: an alternative explanation?
- MP theory: given productivity, competition ensures wages equal MRP.
- Incentive schemes: causality runs the other way (pay → productivity).
- Examples: piece rates (pay per unit of output produced), bonuses,
performance based raises, stock options or profit-sharing plans.
- Efficiency wage models: high pay policies (above “going rate”) may
boost productivity in some circumstances.
- why?
- psychology and gift exchange (Akerlof).
- anti-shirking device: work harder to keep the high wage job.
- high wage policy allows employer to pick the best (selection).
- Incentive stories and “very high pay”:
- Bonuses and stock options can be a large part of very high pay.
- idea is to provide incentives for good performance.
- Tournament model: an incentive model of high pay
- High salaries attached to top positions are like a prize.
- High-performance lower level managers can eventually be
promoted to a top position.
- High salary justified by top manager’s productivity plus increased
productivity of lower level managers who hope to win the
prize.
Trends in income inequality since the early 1980s:
- high growth in incomes of the very highest earners.
- Green, Riddell and St-Hilaire (2017) Income Inequality in Canada
( )
- More generally: World Wealth and Income Database ( )
- Why? What has changed? Maybe:
- Winner-take-all markets and superstars: are more goods like this
than before?
- Incentive pay: more important than in the past?
- Anything else?
- Some views on growth in very high pay:
H. Varian (Chief Economist at Google):
"THE rise in individual inequality that we have seen is due in part to the rise in globalisation. When most businesses were local, the creation of wealth by a business was limited by the geographic range in which the business could operate. But nowadays even a relatively small business can go from local to national and then global operation in a short amount of time. Fortunes can be made by providing goods and services at a low price to a global market of 6 billion people.
Communication costs and computation costs will continue to drop for the foreseeable future, and we will continue to see new billionaires being created as an inevitable side effect of this technological trend. Ocean voyages, railroads and the telegraph, along with the businesses they enabled, created vast amounts of wealth, so we should expect the same from modern communications technologies."
(this fits with a MP theory story)
S. Sumner (Bentley U. writes the blog "Money Illusion"):
"Today the most productive members of society are notthose who produce things, they are those who discover the things that need to be produced. Once you have the blueprint, it is easy to produce many types of software and pharmaceuticals. The big money goes to those who figure out the blueprint, but also to those who allocatecapital to the guy whohas the idea for a Google, or Facebook, or Twitter.In contrast, the technicians who actuallyimplement the vision often earn modest salaries. Thus companiesare “discovered” in much the same way as aniron deposit is discovered by a skilled geologist.
And then there’s globalization, which means decisions about allocating capital can vastly improve productivity even in the old-line industries that were dominant inthe 1960s, when the rest of the world hardly mattered. Finance is not that important in an agricultural economy or even in an economy where the mass production of goods can be done with almost military precision. It becomes extremely important in an economy where it is not at all clear what should be produced, or on what continent that production should take place."
- Alternative stories?
D. Acemoglu MIT: many at the very top are in finance. Was deregulation key?
"politics may have been the key factor in setting in motion the forces that have led to the massive rise in top inequality and also shaped the path of development of the financial industry..."
J. Stiglitz: politics and economics together?
Great wealth→ political influence→ favorable policies → Wealthier!
- Could it partly be incentive problems in top-earner pay setting?
(Board member incentives and CEOs)
- Changes in attitudes toward high pay (A. Atkinson LSE)?
- Is very high pay socially more acceptable than 30-40 years ago?
- Isit mainly an English-speaking thing? (US, UK, Canada, Australia) If
so why haven't the MP stories had the same effect elsewhere?
- G. Mankiw: is speaking English increasingly valuable?
(entertainment, language of business)
Applications of MP Theory: Changes in employment composition over time
- Major shifts have occurred in the composition of employment by industry and
occupation (see tables below):
- move from agriculture to industry
- shift from manufacturing to services
- MRP theory suggests explanations in terms of changes in:
technology, changes in the pattern of product demand.
i.e. factors that shift MRP curves
- MRP rising (shifting up) in growing sectors:
- they can offer higher wages
- workers shift to these booming sectors
- spillover to declining sectors: competition ensures wages rise in declining
sectors (or that declining sectors disappear).
- Can declines in employment in Ontario’s forestry and auto sectors be explained
via changes in MRP?
e.g. falling output prices? relative quality of cars, price competition?
Natural resource depletion, aging capital?
- Housing and financial bubbles (US): effects on employment by industry.
- Theseare demand explanations but supply side considerations may matter too.
e.g. growth in “pink collar” occupations and women’s participation.
- Role of technology in the MP model is limited.
- it can change productivity of a given type of job.
- can have feedback effects on MRP via the effects on output supply and
price.
- But: model does not allow for substitution.
- it doesn’t allow forlabourbeing replaced by other inputs
(the long-run version of the model can allow for this).
An extension: MP theory and Long-term Employment Contracts
- See discussion of deferred compensation (Ch. 13, pp. 388-395)
- Simple model: w=MRP each period.
- What if employer and worker expect the job to be long-term?
- contract need not tie w=MRP in each period.
- over the term of contract:
- Employer: Present value of MRP must cover Present value of wage
costs.
- Worker: Present value of wages under the contract must equal
present value of wages in best alternatives.
(Present value? Value of future payments now)
- Logic of hiring and labour demand decision much the same as in the
simple case!
- Enforcement issues with long-term contracts:
- if w >MRP near the end of contract: employer has incentive to fire.
- if w<MRP near the end of the contract: worker has incentive to quit.
- long-term contracts must deal with these issues.
(see Figures 13.1, 13.2)
Labour Demand in the Long-run: Substitution
- In the short-run model L was chosen given a fixed quantity of other factors of
production.
- Goods can be produced using different mixes of labour and other factors of
production. Long-run model allows choice of L and other inputs.
- Example below: two inputs – ideas generalize to many types of inputs.
- This is suggested by the production function where Q is output:
Q = Q(K, L)
- Isoquant: shows combinations of K and L which can
be used to produce a given level of output.
- slope? - MPL /MP K
(MP = marginal product, subscript L - labour, K-capital)
(Mathematically using calculus, MPs are derivatives:
)
- with diminishing returns to K and L isoquants will be
convex (see Fig. 5.2)
- Also a higher isoquant, means higher output.
- Hiring decision for K and L:
- Use the least cost method to produce the desired output level.
- Cost: determined by technology and factor input prices.
- Can represent costs graphically using isocost lines.
- Let w be the wage and r the rental price of a unit K.
- assume competitive input markets (w, r fixed for the firm).
- Isocost: combinations of K and L which give the
same level of total cost.
Total cost = w L + r K
C0 = wL + rK isocost for some cost level C0
solve for K:
K = (C0/r) - (w/r) L
Slope = -w/r
Intercept depends on level of cost: higher cost, higher
intercept.
- Profit maximizing / cost minimizing choice:
- cost minimization implies producing any given output
at the lowest possible cost.
- implies using the combination of K and L that puts the
firm on the lowest isocost for that isoquant.
- isocost and isoquant will typically be tangent:
- Tangency gives:MPL = w
MPK r
(usually? corner solution possible but not so interesting)
- If: MPL > w
MPK r
hire more L, less K : can hold output constant and reduce cost.
- If: MPL < w
MPK r
hire less L, more K : can hold output constant and reduce cost.
- Note that when cost is minimized the usually MP theory condition
still holds:
For L MRP of L = w
For KMRP of K = r
- Consider the effect of a rise in the wage rate in the long-run:
- rise in w gives a new, steeper set of isocost lines
- holding output constant, the firm chooses a less labour
intensive way of producing output.
- this fall in L is the substitution effect
- At the new combination of K and L cost is higher than
before (output still at its old level).
- firm is likely to reduce its output level.
- this produces an additional fall in L (scale or output effect)
- So:
- High wage relative to the price of machines (or some other