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Economics 202: Intermediate Microeconomic Theory

Economics 202: Intermediate Microeconomic Theory. Should be through Chapter 12 (Chapter 14, Monopoly is next) HW on website, due Tue in class. Numerical Example of Long-run Input Demand.

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Economics 202: Intermediate Microeconomic Theory

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  1. Economics 202: Intermediate Microeconomic Theory • Should be through Chapter 12 (Chapter 14, Monopoly is next) • HW on website, due Tue in class

  2. Numerical Example of Long-run Input Demand • Consider a monopolist with production function Q = L½K ½ and facing D-curve P = 36 - Q, and competitive input prices w = $4, r = $16 K 1. Find L*,K* in terms of w,r, & Q. Set MRTS = ratio of the input prices The cost-minimizing input levels for any level Q are L* = r½w -½Q K* = w½r -½Q Q = 10 TC* 16 2. What is the optimal level of Q? Profits are maximized when MR = MC Use Total Revenue  Marginal Revenue Use Total Cost = wL + rK  Marginal Cost Set MR = MC  36-2Q = 2w ½r ½ 36-2Q = 2. 4½ . 16 ½  Q* = 10 K* = 5 L* = 20 TC* 4 Labor 3. Use answer from (1) to find L*, K*, TC* L*= 20, K*= 5, TC*= 4(20)+16(5)= $160

  3. Numerical Example of Long-run Input Demand • Now suppose that because of a new union contract the w rises to $9. • How do the optimal L*,K* change? K • Isolate the SE. K is relatively cheaper so substitute toward K, keeping Q at 10. L* = r½w -½Q K* = w½r -½Q Lse= r½w -½Q = (4/3)10 = 13.3 Kse= w½r -½Q = (3/4)10 = 7.5 TC at this Lse & Kse goes up: TC = $9(13.3) + $16(7.5) = $240 NB: this is less than if they didn’t economize on the more-expensive L TC = $9(20) + $16(5) = $260 Q = 10 TC* 16 7.5 SE 5 13.3 20 TC* 4 Labor SE • Is MR still = MC? No. 36-2Q = 2w ½r ½  36-2(10) < 2(3)(4)

  4. Numerical Example of Long-run Input Demand • What is the new -max level of output? 36-2Q = 2(3)(4)  Q*new = 6 units • What is the cost-minimizing way to produce any level of Q? Recall L* = r½w -½Q K* = w½r -½Q L* = (4/3)6 = 8, K* = (3/4)6 = 4.5 K Q* = 10 Q*new = 6 • Scale effect of a wage increase is to decrease production level (Q), which means the firm needs less K and less L. 7.5 ScE 5 4.5 • EffectLK Original 20 5 Subst Effect-6.7+2.5 Scale Effect-5.3-3.0 Final Point 8 4.5 8 13.3 20 Labor ScE

  5. Gross Complements or Substitutes • For labor, the SE and the ScE reinforce one another  D-curve for labor is downward-sloping. That’s good. Wage $9 4 D 8 13.3 20 Labor • For capital, the SE and the ScE work in opposite directions. Shock:  Price of Input i Price of Input j • If we  Price of input i: SE > ScE  Gross Substitutes SE < ScE  Gross Complements (notice thatblueandyellowmake green, actually that was total coincidence  ) +2.5 -3.0 D1 D0 Gross Complements Quantity of Input j

  6. Gross Complements or Substitutes • More than 2 inputs • Categories of L & K, energy, raw materials/supplies • Cost-minimizing condition still same: Wskill/MPskill = Wunskill/MPunskill = r/MPK • If two inputs i and j are substitutes in production, they can be Gross Substitutes or Gross Complements • If we  Price of input i: SE > ScE  Gross Substitutes SE < ScE  Gross Complements • Snow-removal firm: let j = skilled workers • If two inputs i and j are complements in production, they must be Gross Complements (no SE, only ScE) Shock:  Price of Input i Price of Input j Gross Substitutes D0 Gross Complements Quantity of Input j

  7. Competitive Firm Example • Assume firm operates in a perfectly competitive output market and perfectly competitive input markets • Let Q = f(K,L) = K1/3L1/3 • Find unconditional factor demand functions and firm supply curve. • Comparative statics

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