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Economics 202: Intermediate Microeconomic Theory

Economics 202: Intermediate Microeconomic Theory. Any questions? Read Ch 10 HW #9 on website, due next Thursday. Long-Run Costs of Production. Capital (K). TC 3 /r. TC 2 /r. slope = -w/r. TC 1 /r. TC 1 /w. TC 3 /w. Labor. TC 2 /w. All inputs are variable

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Economics 202: Intermediate Microeconomic Theory

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  1. Economics 202: Intermediate Microeconomic Theory • Any questions? • Read Ch 10 • HW #9 on website, due next Thursday.

  2. Long-RunCosts of Production Capital (K) TC3/r TC2/r slope = -w/r TC1/r TC1/w TC3/w Labor TC2/w • All inputs are variable • Firm’s costs can be represented by an Iso-Cost line, which identifies all the combinations of (L,K) that can be purchased for a given total cost. • TC = wL + rK • Rewrite to get: K = (-w/r)L + (TC/r) • Y-intercept is TC/r • X-intercept is TC/w • Slope indicates the relative prices of the inputs (slope = -2 says hiring 1 more L, means must buy 2 less K) • Analogy with consumer’s problem • Exception? • Consumers are stuck with feasible set • Firms can increase TC by hiring more inputs and paying for them by selling more output • Assumptions • Homogeneous labor and capital • Perfectly competitive input markets

  3. Least Cost/Max Output • At the tangency point, slope of the isoquant = slope of the isocost line • MPL/ MPK = w/r • Two ways to interpret: 1. “Least-cost way to produce a given Q” If firm decides to produce Q2, the cost-minimizing way is TC2. 2. “Maximum output possible for a given TC” If firm decides to spend TC1, Q1 is the most they can produce. • This is the “Dual” problem to the firm’s “Primal” cost-min problem Capital (K) TC3/r TC2/r slope = -w/r TC1/r Q3=9 A Q2=6 Q1=3 TC1/w TC3/w Labor TC2/w

  4. Output Maximization • Let’s rearrange the equation MPL/ MPK = w/r as follows: MPL= MPK w r • This says that the firm should use K & L in such a way that the additional output per dollar spent on L = additional output per dollar spent on K • Firm decides to spend TC2. What’s the most Q they can make? • At point A: MPL= 100 widgets, w = $20 MPK= 25 widgets, r = $25 • MPL/w = 5 widgets/dollar MPK/r = 1 widget/dollar Capital (K) TC2/r A M Q2 Q1 TC2/w Labor • Firm can increase Q and keep the same total cost: A  M • Spend $1 less on K  lose 1 widget Spend $1 more on L  gain 5 widgets

  5. Cost Minimization • Interpretation #2, rearrange another way: w = r MPL MPK • This says that the last widget made using L should cost the same as the last widget made using K. • Firm decides to make Q1 widgets. What’s the least-cost way to do it? • MPL= 10 widgets, w = $20 MPK= 8 widgets, r = $10 • w/MPL = $2/ widget r/MPK = $1.25/ widget • Firm can decrease TC and still produce Q1 widgets: B  N Capital (K) TC2/r TC1/r N B Q1 TC1/w TC2/w Labor • Produce 1 less widget using L  save $2 Produce 1 more widget using K  costs only $1.25 more

  6. Expansion Path • The long-run Expansion path traces out the least-cost way to produce different levels of Q • As drawn, we’ve assumed that input prices are constant (since the slope of isocost lines do not change) • Cost-minimization is not the same as -maximization •  = TR - TC so cost-minimization is necessary for profit maximization • Cost-minimization occurs at all points on the expansion path, but -max involves choosing the point on the path that yields the most profit. Capital (K) TC3/r TC2/r TC1/r Expansion Path C B Q3 A Q2 Q1 TC1/w TC3/w Labor TC2/w

  7. Long-Run Cost Curves $ • Q = L2/3K2/3 • IRS, CRS, or DRS? • Find LRTC function. • Decreasing, constant, or increasing LRTC? That is, as Q goes up, LRTC does what? LRTC 100 20 Q $/unit MC LRAC Q

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