Chapter 13 Factor Market
Contents: • Factor Demand • Factor Supply • Other Points to be Noticed
In factor markets • Firms demand factors to produce goods • Firms aims at maximizing wealth (by weighing the gain from employing factors against the cost.)
Factor demand is also called derived demand. Because a firm demands factors only if there is a demand for the good it produces.
Symbols: Quantities of factors employed – A, B, C, ... Factor (hire) prices – HA, HB, HC, ... Quantity of the good produced (product) – Q Productprice – P
Marginal factor cost curve Marginal factor cost (MFC) is the cost of employing an additional unit of a factor. (MFC of a factor vs. MC of a good)
Marginal factor cost curve Assumptions: 1. The firm is a price-taker in the factor market. 2. It cannot affect the prevailing factor price (H) & hence MFC isa constant equal to H. MFC = H (=AFC)
$ H 0 Factor A Shape of factor supply curve, MFC curve and AFC curve • As the firm can employ as many units of • the factor as it desires without affecting H, • the factor supply curve as well as the MFC curve & the AFC curve are horizontal lying at H. Factor Supply Curve = MFC curve = AFC curve
Marginal revenue product curve Definitions: Marginal revenue product(MRP) is the gain from employing an additional unit of a factor. (MRP of a factor vs. MR of a good) Average revenue product (ARP) is the gain from employing a unit of a factor on average. Value of marginal product (VMP) VMP = MP xP
Derivation: When a firm employs an additional unit of factor, its output will by MP and its revenue will bymarginal revenue product MRP = MP x MR
Derivation: • In the product market, • if the firm is a price-taker, • MR = PMRP (= MP x MR) =VMP (= MP x P) • if the firm is a price-searcher, • MR < PMRP (= MP x MR) < VMP (= MP x P)
Output produced Output produced MRP=MP xMR ARP=AP xAR AP x AR=ARP MPx MR=MRP AP MP 0 0 Factor A Factor A Shape of MRP curve and ARP curve Derivation of MRP and ARP curve
H1 Derivation of the factor demand curve At H1 (=MFC) MRP (gain) MFC (cost) The firm will not employ any units of the factor.
M N H2 A1 A2 At the factor price of H2 • At A2, • ARP < AFC • Factor employment at A2 brings losses. The employment is not worthwhile. • At M,MRP curve cuts MFC curve from below. • Either an or in factor employment would raise wealth. • A1is wealth- minimizing. • At N,MRP curve cuts MFC curve from above. • Either an or in factor employment would reduce wealth. • A2is wealth- maximizing MFC = AFC
H3 T A3 At the factor price of H3 • At point T, MRP curve cuts MFC curve from above • At A3, ARP > AFC • Factor employment at A3 can maximize wealth.
Equilibrium conditions of factor employment 1. MRP = MFC 2. MRP curve cuts MFC curve from above (to determine the best employment level) 3. ARP AFC (to determine if it is worth employing)
Factor Demand Curve • Provided that ARP AFC, the wealth-max. level of factor employment is A at which MRP=MFC=H. • So the factor demand curve is the portion of the MRP curve lying below the max. point of the ARP curve.
Market factor demand curve • A factor is demanded by many different firms, e.g., clerks are employed in hospitals, schools, accounting firms, etc. • So the market factor demand curve is equal to the horizontal sum of factor demand curves of all the firms in the market.
Budget line of a price-taking factor supplier Income N Numerical value of the slope = Factor price (e.g., hourly wage rate) M I0 Resource for own use (e.g., leisure) R 0 R0 (e.g., 24 hours)
Indifference map of a factor supplier For a resource with reservation use (a good) The indifference curves are convex to the origin. Why?
I* Amount of factor supplied R* Equilibrium of a factor supplier A resource with reservation use (a good)
A2 A1 Substitution effect and income effect of a price change • The effect of a change in price can be decomposed into substitution effect and income effect. Price effect • in price • Budget line tilts upward
S.E. A’ Substitution effect • Factor pricecost of retaining the resource forone’sown usethe individual will keep fewer units & supply more units in the factor market. • By the S.E., factor price and quantity supplied arepositively related. A1
I.E. Income effect If the resource with reservation use is a superior good, factor price individual earns he keeps more units and supply fewer units in the factor market. Factor price and quantity supplied arenegatively related. S.E. A1 A’ A2
Backward bending factor supply curve • When the factor price is low, the Qs is small. Even if the factor price by 10%, the in income is rather small. • At the beginning, the individualstill owns a large amount of the resource for his own use. • WhenH rises, the individual is willing to supply more, i.e., income effect (A) < substitution effect (A). The factor supply curve is upward sloping.
H’ S.E. > I.E. • When factor price is low, a rise in factor price from H1 to H’ will raise the factor supplied S.E. > I.E. Upward sloping factor supply curve
Backward bending factor supply curve (con’t) • When the factor price is high, the Qs is large. Even a 10% rise in income will raise the income by a very large amount. • The individual now owns only a very small amount of the resource for his own use. • This time, when H rises, the individual desires to keep more units of the resource for his own use & supply less, i.e., income effect (A) > substitution effect (A). The factor supply curve is downward sloping.
S.E. < I.E. • When factor price ishigh (above H’), a rise in factor price from H’ to H2 will lower the factor supplied S.E. < I.E. H’ Backward bending factor supply curve
Q13.3: If the resource with reservation use is an inferior good, what will be the shape of the factor supply curve of an individual?
Total receipt (TRP = ARP x L) $ Total payment to labour (W x L) Total payment to other factors (TRP – W xL) ARP W MFC=AFC MRP Quantity supplied of labour 0 L Functional distribution of income
A0 A0+1 Factor employment and marginal revenue product When the firm employs one more unit of factor A MPA and MRPA (along the curve)
As more units of factor A are employed, factor B will be used more intensively and productively MRP curve of factor B shifts upward B0
Malthus’ law of population – a myth? Malthus’ law of population • Population living standard of man (since MP & AP ) • Population cease to expand when AP to the subsistence level
Why is the law not confirmed? • Capital accumulation • Investment on education • Technological improvement • Institutional improvement • Specialization due to globalization MP & AP curve shifted upward greatly & rapidly. Average living standard rose with population growth.
Income differential In a price-taking factor market, price of a factor(factor income) is determined by the market D & S of the factor.
Income differential In a price-taking factor market, market demand is determined by productivity of the factor (e.g., ability, training and working experience) price of the product (depends on its D & S), discrimination (e.g., against the female, youngster & minority)
Income differential In a price-taking factor market, market supply is determined by amount of capital accumulated size & structure of population geographical distribution of labour government policies power of trade union
If the factor market isprice-searching, (or controlled by a central authority / an institution) factor priceis NOT determined by the market D & S of the factor H may not reflect the productivity of the factor i.e., H MRP.
Correcting Misconceptions: 1. MRP is the same as VMP. 2. The demand curve for a factor is the MRP curve. 3. If a firm is a price-taker in a factor market, the factor demand curve is horizontal. 4. Substitution effect must be negative.
Correcting Misconceptions: 5. The higher the factor price, the larger the quantity supplied of a factor. 6. As the average living standard rises with population growth, the law of diminishing returns is falsified. 7. The hire price of a factor must reflect its marginal productivity.
Survival Kit in Exam:Question 13.1: Presently, a firm employs five workers. When the workers are on their sick leave, the value of their output drops. The table below shows the situation. If the wage rate is $650, how many workers should the firm employ?
Survival Kit in ExamQuestion 13.2:Suppose a firm employs only two factors, land and labour. The total return is distributed among them. If the firm fires several workers, what will happen to(a) the marginal product of labour and that of land?(b) the total return of labour and that of land?