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Labour Demand (Short-Run (SR) (Profits need not be 0, Firm hires workers…
Labour Demand
Short-Run (SR)
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Firm hires workers to the point where w = VMPE (K is fixed).
Note: Since VMPE is a quadratic, we take the downward-sloping portion of VMPE and equate that to wages. Thus, we can treat VMPE as downward-sloping.
SR labour demand curve is downward sloping: Additional workers are costly, and alter average production due to Law of Diminishing Marginal Returns.
Stopping Rule on Output
- Profit-maximising firm should product to the point where MC = MR. Note that MC = w/MPE, MR = p.
- Marginal productivity condition: Hire labour to the point where w = VMPE.
Critiques of Marginal Productivity Theory:
- Theory bears little relation to the way employers make hiring decision
- Assumptions of theory are not very realistic (e.g. shape of production function)
Long-Run (LR)
Profits = 0 (otherwise, other firms will enter.)
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Isoquant curves: Describes possible combinations of E and K at the same level of output.
- K against E
- Slope = Marginal rate of technical substitution (MRTS) = Change in K/Change in E = -(MPE/MPK)
- Convexity of isoquant wrt origin due to diminishing marginal returns
- If we have straight isoquants, it means we have perfect substitutes. = elasticity of substitution = infinite
- If we have Leontief curves, it means we have perfect complements. =elasticity of substitution = 0
Isocost lines: Indicates all K-E bundles that exhaust a specified budget for the firm (e.g. C = wE + rK)
- In other words, isocost lines indicate equally costly combination of inputs.
- Higher isocost lines indicate higher costs.
- K against E
- Slope = -w/r
LR Labour Demand
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Substitution effect
Firm takes advantage of w/r changes to rearrange its mix of inputs, employing more/less K/E while holding output constant.
Elasticity
Since firm can vary K and E in LR (in SR, K is fixed), LR labour demand is more elastic than SR demand curve.
Elasticity of substitution = (%change K/L)/(%change w/r)
= % change in K-E ratio given a % change in price ratio
e.g. if elasticity of substitution = 5, then 10% increase in w/r leads to a 50% increase in K/L
Marshall's Rules
Labour demand is more elastic if:
- Elasticity of substitution is greater
- Elasticity of demand for firm's output is greater (wage increase -> equilibrium MC increases -> p increases -> consumer demand falls -> demand falls sharply if elasticity is high -> labour demand declines sharply)
- Labour accounts for higher % of total production costs (increase in w will have larger impact on equilibrium MC)
- Elasticity of supply of other factors of production (e.g. K) is greater (i.e. it's cheap to substitute it to labour)
Note: Labour demand is more elastic if you use more labour.
Cross-elasticity of factor demand = (%change in input)/(%change in wage)
- If XES >0, the two production inputs are substitutes
- If XES <0, the two production inputs are complements
Note: Demand curve for input i changes when price of another input changes (e.g. if price of substitute increases, demand curve increases).
Production Function
Marginal product of labour (MPE) = Change in output resulting from hiring an additional worker, holding constant the quantities of other inputs.
Marginal product of capital (MPK) = Change in output resulting from employing 1 additional unit of capital, holding constant the quantities of other inputs.
Optimisation problem
Profit Maximisation
Value of marginal product of employment (VMPE) = Marginal product of labour x dollar value of output = p*MPE
This indicates dollar revenue from hiring an additional worker, keeping capital constant.
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Cost Minimisation
Firm chooses least-costly combination of K and E to produce given output level. Least costly choice is where isocost line is tangent to isoquant.
MRS = ratio of input prices
i.e. MPE/MPK = w/r
Note that this is where slope of isoquant = slope of isocost
Optimal quantity is where MC = p (marginal cost of production = output price), where MC now refers to both K and E
At optimum, cost minimisation = profit maximisation.
MPE = w/p
MPK = r/p
In other words, productivity of each input = real price!