# Chap31 - Econ. 102. Chapter 3-1 Demand for Labor...

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Unformatted text preview: Econ. 102. Chapter 3-1 Demand for Labor Proposition 1: The proﬁt-maximization condition of inputs for a perfectly competitive ﬁrm comes when the marginal product times the output price equals the price of input: Marginal product of labor x output price = price of labor = wage rate Marginal product of capital x output price = price of capital = rental price of capital and so forth. Example: Assumptions (1) The firm is a price taker in the output and the input market. (2) Y = F(L, K), MPL E dY/dL > 0, MPK E dYx’clK (3) The law of diminishing marginal returns applies, i.e., dZYr’sz < 0. (4) The objective of the firm is to maximize proﬁt. Max H=PY-—WL—RK=PF(L,K)—WL-RK Numerical Example: P = 10, W = 50, K =1, R = 5 L K Y MPL PxMPL W TR=PY C = WL+RK H = TR — C 0 l 0 — - 50 0 5 —5 l l 12 12 120 50 120 55 65 2 1 19 7 70 50 190 105 85 3* l 24 5 50 50 240 155 35 4 l 28 4 40 50 280 205 75 5 l 30 2 20 50 300 255 45 Gofden Rule: (i) PXMPL > w 3 Lt, (ii) PXMPL < w : Lt, (iii) PXMPL = w => L*. PxMPL = w = 50, L* = 3,1113): I1 = 85. Graph: map w {‘36 All? Nb W —_.-4-o~w..-.-._~H Proposition 2: The proﬁt—maximization condition of inputs for a perfectfy competitive ﬁrm comes when the marginal product times the output price equals the price of input: Marginal product of labor = real wage rate Marginal product of capital = rental price of capital and so forth. L K Y NIPL WIP TR=PY C = WL-I—RK 11 = TR — C 0 1 0 - 5 O 5 -5 l 1 12 12 5 120 55 65 2 1 19 7 5 190 105 85 3* 1 24 5 5 240 155 85 4 1 28 4 5 280 205 25 5 l 30 2 5 300 255 45 Gofden Rule: (i) MPL > WP :» LT, (ii) MPL < WHP : Li, (iii) MPL : wrP : L*. MPL= wrp = s, L* = 3, max n: 85. Graph. M P k n! H P .2 ill “x l 1 l l E l ‘2 3i \ all 6 ‘5. l E ...
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## This note was uploaded on 09/08/2010 for the course ECON 102 at San Jose State University .

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Chap31 - Econ. 102. Chapter 3-1 Demand for Labor...

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