Transcript Factor Markets

Chapter 15
Factor Markets
Work is of two kinds: first, altering the
position of matter at or near the earth’s
surface relative to other matter; second,
telling other people to do so.
Bertrand Russell
Chapter 15 Outline
Challenge: Should You Go to College?
15.1 Factor Markets
15.2 Capital Markets and Investing
15.3 Exhaustible Resources
Challenge Solution
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Challenge: Should You Go to
College?
• Background:
• Going to college is expensive.
• In the 2011–2012 school year, half of all
18 to 24-year-old undergraduate
students borrowed money to pay for
college.
• Question:
• Is going to college worth it?
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15.1 Factor Markets
• Factor markets refer to the markets where labor (L) and
capital (K) are bought and sold or rented.
• Factor markets are competitive when there are many small
sellers and buyers.
• Factor markets from earlier chapters:
• Labor supply determination via labor-leisure model (Ch. 5)
• Firm input choices via profit maximization (Chs. 6 & 7)
• Competitive supply determination for general firm (Ch. 8)
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15.1 Factor Market in Short Run
• A firm’s SR production function can be expressed solely in
terms of labor, q = q(L), because capital is fixed in the SR.
• Revenue is a function of production and the firm’s objective is
to maximize profit by choosing L in the SR:
• FOC:
• Simplifies:
• The firm chooses L so additional revenue from employing last
worker equals wage paid to that last worker.
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15.1 Factor Market in Short Run
• The marginal revenue product of labor (MRPL),
sometimes called the value of the marginal product, is
the additional revenue generated by the last unit of
labor.
• In a competitive market:
• This is the firm’s SR labor demand function.
• The MRPL shows the maximum wage that a firm is
willing to pay to hire a given number of workers.
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15.1 Competitive Factor Market
in the Short Run
• The profit-maximizing number of workers is given by
the intersection of supply and demand (MRPL).
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15.1 Competitive Factor Market
in the SR: Effect of Wage Change
• Graphically, we can see that more workers are hired as
the wage falls.
• Mathematically, we prove this result with comparative
static analysis.
• Differentiate MRPL equation with respect to the
wage:
• Rearranging terms:
• This derivative is negative if the firm is operating where
there are diminishing marginal returns to labor.
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15.1 Noncompetitive Firm’s SR
Factor Demand Curve
• How does market power in the output market affect
factor market equilibrium?
• Less of a factor is sold than if all firms were
competitive.
• Accounting for market power, the marginal revenue
product of labor function is:
• For an identical MPL curve, a Cournot dupoly firm’s
labor demand curve lies above that of a monopoly,
but below that of a competitive firm.
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15.1 Noncompetitive Factor Market
• The labor demand curves for different market structures.
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15.1 Factor Demand
in the Long Run
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15.1 A Competitive Firm’s Long Run
Factor Demand Curve
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15.1 Comparing Short Run
and Long Run Labor Demand Curves
• LR labor demand is flatter because firms can
vary all inputs.
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15.1 Competitive Factor Markets
• A factor market demand curve is the
horizontal sum of the factor demand curves
of the various firms that use the input.
• Inputs such as capital and labor are used in
many markets.
• Derive the labor demand curve for each
output market and then sum across output
markets to obtain the factor market demand
curve.
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15.1 Firm and Factor Market
Demand
• Summing individual factor demand curves (with price
changes) to derive market demand:
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15.2 Capital Markets and Investing
• When renting durable goods or workers’ services, a firm
chooses a quantity that equates current marginal cost
and current marginal benefit.
• If the capital good must be bought or built rather than
rented, then a firm must compare current cost of
capital to future higher profits associated with the
investment.
• Such comparisons involve both stocks and flows.
• A stock is measured independently of time (e.g.
wealth).
• A flow is measured per unit of time (e.g. income).
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15.2 Capital Markets and Investing
• An interest rate is the percentage more that must be
repaid to borrow money for a fixed period of time.
• People value having a dollar today more than having a
dollar in the future, so some future offering would have
to be inflated:
• A discount rate reflects the relative value an individual
places on future consumption compared to current
consumption.
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15.2 Capital Markets and Investing
• Many people and firms pay for a new purchase by
making monthly payments over time.
• One way to evaluate this investment is to compare the
present value (PV) of the flow of payments to the PV of
the item purchased, the stock.
• If the firm makes a future payment of f per year for t
years at an interest rate i, the PV of this flow of
payments is:
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15.2 Net Present Value Approach
• A firm should make an investment only if the PV of the
expected return exceeds the PV of the costs.
• A firm should make an investment only if the net present
value is positive: NPV = R – C > 0.
• If in year t of T years, revenue is Rt and cost is Ct, then the
firm should invest if:
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15.2 Internal Rate of Return
Approach
• The internal rate of return (irr) is the discount rate such
that the net present value of an investment is zero.
• Solve the following for irr:
• where f is a steady stream of profit paid forever
• It pays the firm to borrow to make the investment if the
internal rate of return on that investment exceeds that of the
next best alternative: irr > i.
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15.3 Exhaustible Resources
• Discounting plays an important role in decision making
about how fast to consume exhaustible resources,
nonrenewable natural assets that can only be depleted.
• Examples: oil, gold, copper, uranium
• If the cost of mining an exhaustible resource is m and it
could be sold for p1 this year or p2 next year, then when
should you sell it?
• Sell it all this year if p1 – m > (p2 – m) / (1+ i )
• Sell it all next year if p1 – m < (p2 – m) / (1+ i )
• Sell it either year if p1 – m = (p2 – m) / (1+ i )
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15.3 Exhaustible Resources
• How does the price of an exhaustible resource change
over time?
• The price of an exhaustible resource changes from year
to year according to:
• In order to be indifferent between selling the resource
this year and next, this year’s price must be higher.
• It must be higher by a specific amount.
• That amount is the value of selling today and investing
the proceeds: i (pt – m)
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15.3 Exhaustible Resources
• The gap between resource price and marginal cost,
pt – m, grows exponentially with the interest rate.
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15.3 Exhaustible Resources
• The price of an exhaustible resource will rise if all
of the following conditions are met:
1.Resource is scarce
2.Resource has a constant marginal cost of extraction
over time
3.Resource is sold in a competitive market
• Most exhaustible resources have experienced long
period with falling or constant real prices. Why?
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15.3 Exhaustible Resources
• The real price of an exhaustible resource may fall or
remain constant due to:
1.Abundance
•
If the good is so abundant that the initial gap between price
and marginal cost is zero, the gap does not grow.
2.Technical progress
•
The marginal cost of mining has been reduced by technical
progress over time.
3.Changing market power
•
Changes in market structure can result in either a rise or fall
in the price of an exhaustible resource.
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Challenge Solution
• Individuals may choose to invest in education in
order to raise their productivity and future
earnings.
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Challenge Solution
• If the discount rate is less than 10.42%, then the
present value of earnings for a college grad is
greater than that of a high school grad.
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Figure 15.6 First-Year Price in a Two-Period
Model
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