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Chapter 5 LR Demand for Labor • Long run (LR): period of time that is long enough for firm to vary both K and L (in response to es in: factor prices/demand, technology). • Decision: pick K/L combo to produce Q at minimum cost; based on two factors: – 1. Substitutability of K and L: given by production function. – 2. Relative prices of K and L. Production Function • Shows technological constraints. – Relationship between es in K and L and es in Q; – Also shows how can K and L keeping Q constant. • Isoquant: “iso” means same. – Shows substitutability between K and L, keeping Q fixed. – MRTS: marginal rate of technical substitution: measures the reduction in K needed if labor is by one unit and Q held fixed. – Convex: MRTS diminishes as move down isoquant. Fixed Proportions Production Function • Only one combination of K and L can be used to produce each Q level. • No substitutability (MRTS=0). • Only relevant points are the “corner” points, with least-cost combination of K/L for each Q shown as line from origin thru these corner points. Factor Prices • Price of labor = wage = w. • Price of capital = “rental rate” of K = r. • Isocost line: given factor prices, shows all combinations of K and L that firm could purchase with specific $ expenditure = E. • Given E1: – If only buy L: E1/w1 = L1 units. – If only buy K: E1/r1 = K1 units. Features of Isocost Line • 1. Slope = -w1/r1 = constant. • (Derive with rise/run, where the E1 cancel.) • 2. For given factor prices: if E shift isocost parallel to right (no slope). • 3. If K or L slope (so an intercept changes). • Example: If w w/r; so steeper isocost line; es horizontal intercept. Cost-Minimizing Employment Level • Assume for now: already know the firm’s profit-maximizing Q level (where P=MC); so given this Q*, pick K/L combo. • Cost-minimizing K/L combo: Occurs at tangency: where slope of isocost = slope of isoquant; • MRTS = -w/r. • Equilibrium condition: rate that technology says K/L can be traded off equals rate market says K/L can be traded off (based on factor price ratio). Firm’s Profit-Max Choice of Q* • Firm picks Q* at point where the market price equals MC of production; P = MC. • Price line is horizontal line; also referred to as Demand curve (perfectly competitive firm faces perfectly elastic D curve since it can sell all it wants to at market P). • If w, MC too (MC shifts). Firm Makes Two Distinct Decisions • Decision #1: profit-maximizing choice of output = Q*. • Decision #2: given this Q*, cost-minimizing choice of K and L. • Effect of wage: – 1. Shifts MC curve so es Q*. – 2. (w/r) so pivots isocost line; so es horizontal intercept too. Effect of Wage on Firm’s Desired Employment Level • Key: w for just this firm. • Remember: wage affects choice of Q* first, then affects choice of K and L. • wage: shifts MC curve to left Q*. • Since Q*, must be on isoquant farther to left. • This w is a (w/r) so isocost line gets steeper (pivot to left around same vertical intercept). • See will change both K and L in LR. LR Demand Curve for Labor • Connect the two long run points from previous example. • Note: LR DL curve is flatter (more elastic) than SR DL curve because in the LR, the firm has more chances of substitution since K is not fixed. • In LR: DL is more responsive to wage changes. Determinants of Elasticity of DL • Why care? • Helps to predict employment effects of various policies: – wage subsidy. – unions pushing for higher wages. – increase in minimum wage. Four Laws of Derived Demand • DL will be more elastic (ceteris paribus): – 1) the larger the price elasticity of demand for the product. – 2) the greater the share of labor cost as a percentage of TC. – 3) the greater the ease of substitution in production between K and L. – 4) the greater the elast of S of other competing factors like K. Technological Change and Labor Demand • Remember: technological change will result in entirely new production function. • Technological change has two effects on employment; net impact depends on which is bigger: – 1) DL: better technology allows firms to produce given Q with fewer workers. – 2) DL: better technology costs of production product prices and product sales. – In general: winners and losers. Displaced Workers • Issue: Even if technological change leads to overall increase in employment, some workers lose jobs. • These workers referred to as displaced workers. • Policies include: – 1) regular UI. – 2) targeted training programs. – 3) legislation requiring advance notice of mass layoffs.