Source: Lecture Notes of Prof. Guoqiang Tian, Texas A&M University
Tags: factor markets, input demand, marginal value product, MVP, marginal revenue product, MRP, monopsony, income-leisure choice, labour supply, backward-bending supply curve, substitution effect, output effect, economic rent, interest rate, real vs nominal interest, investment demand, wage differentials, human capital
This section shifts from product markets to input (factor) markets. A competitive firm hires labour up to the point where the marginal value product of labour equals the wage rate. A monopolist uses marginal revenue product instead. The supply of labour emerges from the worker's income-leisure trade-off and can bend backward at high wages. Wage differences arise from equalising differentials, human capital investment, and ability. Rent, interest, and profit round out the factor-income picture, with the interest rate determined by the interaction of saving supply and investment demand.
Marginal value product of labour (MVPL)
The marginal product of labour multiplied by the output price. MVPL = MPL * Px. This is the competitive firm's demand curve for labour (with other inputs fixed).
Marginal revenue product of labour (MRPL)
The marginal product of labour multiplied by marginal revenue. MRPL = MPL * MRx. This is the monopolist's demand curve for labour. Since MRx < Px for a monopolist, MRPL < MVPL at every employment level.
Input hiring rule (competitive firm)
Hire labour up to the point where MVPL = W (the wage rate). Equivalently, MPL * Px = W, which rearranges to W/MPL = Px, or MC = P (the familiar output-side condition).
Input hiring rule (monopolist)
Hire labour up to the point where MRPL = W.
Substitution effect (input demand)
When the wage falls, the firm substitutes the now-cheaper labour for capital, increasing employment (holding output constant).
Output effect (input demand)
When the wage falls, marginal cost decreases, so the firm expands output, further increasing employment.
Income-leisure choice
The worker chooses between income (from working) and leisure. The budget constraint is I + W L = W 168 (for a week), where L is leisure hours and W is the hourly wage.
Backward-bending labour supply curve
At low wages, the substitution effect dominates: a higher wage encourages more work. Beyond some wage level, the income effect dominates: the worker is wealthy enough to "buy" more leisure, so hours worked decrease as the wage rises.
Monopsony
A market with a single buyer of an input. The monopsonist faces the upward-sloping market supply curve for the input. The marginal cost of hiring an additional worker exceeds the wage rate (MCL > W), because raising the wage for the new hire means raising it for all existing workers too.
Economic rent
The portion of payment to an input supplier that exceeds the minimum amount needed to retain the input in its current use. When the supply curve is vertical, the entire payment is economic rent. When the supply curve slopes upward, rent is the area above the supply curve and below the price.
Interest rate
The price paid by borrowers for the use of funds, or the rate of return earned by capital. Determined by the interaction of saving supply and the total demand for funds (consumer loans plus investment demand).
Real interest rate
The nominal interest rate minus the rate of inflation. Measures the true purchasing-power return on savings or cost of borrowing.
Rate of return on investment (g)
For a one-period investment: C = R/(1 + g), where C is cost and R is gross return. Investment expands until g equals the market interest rate.
Equalising wage differentials
Wage differences that compensate workers for non-monetary differences in job attractiveness (danger, unpleasantness, location).
Human capital
Skills and training acquired through education and experience. Differences in human capital investment explain part of wage inequality.
With capital fixed, the firm's demand for labour is the MVPL curve. The firm hires workers until the last worker's contribution to revenue just covers their wage.
Example: if Px = $10 and the daily wage = $30, the firm hires workers until MPL * 10 = 30, i.e. MPL = 3.
When the wage falls, two effects increase labour demand:
Substitution effect: cheaper labour replaces capital.
Output effect: lower wage reduces MC, firm expands output, needs more of all inputs.
Both effects work in the same direction, so the firm's demand curve for labour always slopes downward.
A monopolist hires where MRPL = W. Because MR < P, the MRPL curve lies below the MVPL curve at every point. So a monopolist employs less labour than a competitive industry would at the same wage. This is consistent with the result that monopolists produce less output.
The industry demand for an input is not simply the horizontal sum of firm demands. When all firms expand output together, the product price falls, which shifts each firm's MVPL curve down. The true industry demand curve is steeper (less elastic) than the sum of individual firm demand curves.
When several industries employ the same input, workers (or capital) will migrate toward the higher-paying industry. This process tends to equalise the input's price across industries.
The worker's budget constraint: I = W * (168 - L), or I + WL = 168W.
At the optimum, MRS of leisure for income equals the wage rate: MRS = W.
Example: if U = L^a I^b with a + b = 1, then L = 168a/(a + b) = 168a. Leisure (and therefore hours worked) is independent of the wage rate, producing a vertical labour supply curve.
At low wages, the substitution effect dominates: a higher wage makes leisure more expensive, so the worker works more.
At high wages, the income effect dominates: the worker is sufficiently well-off to "buy" more leisure, so hours worked decline.
The market supply curve may also bend backward, slope upward, or be vertical, depending on the aggregation of individual supply curves.
A single buyer of an input faces the market supply curve. Key result: MCL > W because hiring one more worker raises the wage for all workers.
The monopsonist hires where MCL = MVPL (or MRPL if it also has monopoly power in the output market). Employment and wage are both lower than under competitive input conditions.
Analogy with monopoly: a monopoly restricts output to raise price; a monopsony restricts employment to lower wages.
Equalising differentials: less attractive jobs pay more to compensate.
Human capital: higher training costs justify higher wages (e.g. engineers vs. clerks).
Ability: innate differences in skill (e.g. aptitude for science and maths).
When supply is perfectly inelastic (vertical), the entire payment is rent. When supply slopes upward, rent is the area above the supply curve below the equilibrium price. Rent measures the gains from voluntary exchange for input owners. The more inelastic the supply, the larger the rent as a share of total payment.
The interest rate equilibrates the supply of saving with the total demand for funds (consumer borrowing + investment).
Investment demand: firms invest as long as the rate of return on capital exceeds the interest rate. As investment expands, returns diminish, so the investment demand curve slopes downward.
For a one-period investment, C(1 + g) = R, so g = (R - C)/C. For multi-period investments: C = R1/(1+g) + R2/(1+g)^2 + ... + RT/(1+g)^T.
Risk: higher default risk commands a higher rate.
Duration: longer loans typically carry higher rates.
Administrative costs: small loans cost more per pound to service.
Tax treatment: varies across types of income.
Real interest rate = nominal interest rate - inflation rate.
MVPL = MPL * Px (competitive firm's input demand)
MRPL = MPL * MRx (monopolist's input demand)
Hiring rule (competitive): MVPL = W
Hiring rule (monopoly): MRPL = W
Income-leisure budget: I + WL = 168W
One-period rate of return: g = (R - C) / C
Multi-period: C = sum of Rt / (1+g)^t
Real interest rate = nominal rate - inflation rate
⚠️ The input hiring condition MVPL = W is equivalent to the output condition P = MC. Be able to show the algebraic equivalence (W/MPL = MC = P).
⚠️ A monopolist's input demand (MRPL) lies below MVPL. Monopolists hire less labour and produce less output.
⚠️ The backward-bending labour supply curve is a classic exam topic. Know that the substitution effect encourages more work (leisure is more expensive), while the income effect encourages less work (the worker can afford more leisure).
⚠️ In monopsony, MCL > W. The firm exploits its market power by paying a wage below the worker's marginal value product.
⚠️ Economic rent is the area above the supply curve below the price. When supply is vertical, all payment is rent. This is distinct from the everyday meaning of "rent."
⚠️ Real vs. nominal interest rates: the real rate is what matters for economic decisions. Real rate = nominal rate - inflation.
Q: A competitive firm sells output at $10 per unit. MPL for the 20th worker is 3.5. The wage is $30. Should the firm hire the 20th worker?
A: MVPL = 3.5 * $10 = $35. Since MVPL ($35) > W ($30), yes, the firm should hire the 20th worker. It adds more to revenue than it costs.
Q: Why does a monopolist hire fewer workers than a competitive industry, all else equal?
A: The monopolist's demand for labour is MRPL = MPL MR, which lies below the competitive firm's MVPL = MPL P (because MR < P for a monopolist). At any given wage, the monopolist's hiring rule yields fewer workers.
Q: Explain why the labour supply curve might bend backward.
A: At low wages, the substitution effect dominates: a wage increase makes leisure more expensive, so the worker substitutes toward work. At high wages, the income effect dominates: the worker is wealthy enough to value additional leisure more than additional income, so hours worked decline as the wage rises further.
Q: What is the difference between economic rent and the everyday meaning of rent?
A: Everyday rent is a periodic payment for the use of a durable asset. Economic rent is the portion of any input's payment that exceeds the minimum needed to keep it in its current use. For a factor with perfectly inelastic supply (e.g. uniquely talented athlete), the entire payment is economic rent.
Q: A firm borrows $1,000 and repays $1,100 after one year. The inflation rate is 5%. What are the nominal and real interest rates?
A: Nominal rate = (1,100 - 1,000) / 1,000 = 10%. Real rate = 10% - 5% = 5%.
Q: In a monopsony, why is the marginal cost of labour greater than the wage?
A: The monopsonist faces an upward-sloping supply curve. To hire one more worker, it must raise the wage not just for the new worker but for all existing workers. The extra cost of the new hire includes both their wage and the wage increase paid to every previous worker. So MCL > W.
factor markets, input markets, labour demand, marginal value product, MVP, marginal revenue product, MRP, derived demand, hiring rule, substitution effect in input markets, output effect, income-leisure choice, labour supply, backward-bending supply curve, monopsony, single buyer, wage determination, equalising wage differentials, human capital, ability, economic rent, quasi-rent, interest rate, real interest rate, nominal interest rate, investment demand, rate of return, saving, time value of money, wage differentials, ECON 323, intermediate microeconomics