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factor_demand.pdf - Lecture notes on factor demand

# factor_demand.pdf - Lecture notes on factor demand - Factor...

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1 1 Factor Demand Key questions: - How does input price affect input demand by the firm? - How does input price affect output level? 2 Optimal Factor Usage Q = f(K,L) π = TR(q) - TC(q) = TR(K,L) - TC(K,L) ∂π / K = TR/ K - TC/ K = 0 TR/ K = TC/ K ∂π ∂π / L = TR/ L - TC/ L = 0 TR/ L = TC/ L Firm adds additional units of each factor until the incremental revenue gain equals the cost of the additional input

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2 3 Part 1: How does a change in input use affect revenue? TR/ L = [ TR/ q] × ∂ q/ L = MR × MP L =MRP L The marginal revenue product of labor (MRP L ) is the extra revenue gained by selling the output that the extra input produces The value of marginal product of labor is defined as VMP L = P × MP L 4 Part 2: How does a change in input use affect cost? TC/ L = w for a competitive market In a competitive market, the firm can purchase as many units of L as wanted at price w In the more general case, TC/ L = marginal expense of labor
3 5 First-order conditions for profit-maximization TR/ L = MRP L = ME L = TC/ L For a competitive input market, ME L =w and key condition is MRP L = MR × MP L = w If the firm sells its output in a competitive output market, then MR = P, so key condition reduces to VMP L = P × MP L = w Remember to distinguish between competition in input and output market 6 What happens to output and input level when a factor price changes? As in consumer theory, we decompose the effect into a substitution and output effect 1) Substitution effect If the price of L falls, the firm will adjust input use from A to B holding constant q 1 • ∂ L/ w < 0 if we hold output constant, i.e., w L A B C handptdwn handptdwn handptdwn q 1 q 2 K L

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4 7 Effect of a Factor Price Change (Continued) 2) Output effect firm increases output and moves to C C implies even more labor is use if input is not inferior substitution and output effects reinforce one another A B C handptdwn handptdwn handptdwn q 1 q 2 K L 8 Effect of a Factor Price Change (Continued) Change in w changes costs and expansion path In general, a decline in wages implies a decline in MC Therefore, P=MC at a higher level of output Price q MC MC’ q 1 q 2
5 9 Cross-Price Effects Have Ambiguous Effect on Input Use If wages fall, it is unclear whether demand for capital will rise or fall The substitution effect is generally negative: K/ w is negative if we hold output constant, since the firm substitutes towards the relatively cheaper input The output effect is positive, however, and may result in increased usage of K Not responsible for mathematical derivation of substitution and output effects 10 What Factors Affect the Own Input Demand Elasticity?

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