# Economics 202: Intermediate Microeconomic Theory 1.Should be through Chapter 12 (Chapter 14, Monopoly is next) 2.HW on website, due Tue in class.

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Economics 202: Intermediate Microeconomic Theory 1.Should be through Chapter 12 (Chapter 14, Monopoly is next) 2.HW on website, due Tue in class

Numerical Example of Long-run Input Demand Consider a monopolist with production function Q = L ½ K ½ and facing D-curve P = 36 - Q, and competitive input prices w = \$4, r = \$16 K LaborTC* 4 TC* 16 K* = 5 Q L* = 20 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* = r ½ w -½ Q K* = w ½ r -½ Q 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 ½ r ½ 36-2Q = 2. 4 ½. 16 ½  Q* = 10 3. Use answer from (1) to find L*, K*, TC* L*= 20, K*= 5, TC*= 4(20)+16(5)= \$160 = 10

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 LaborTC* 4 TC* 16 5 Q = 10 20 7.5 13.3 Isolate the SE. K is relatively cheaper so substitute toward K, keeping Q at 10. L* = r ½ w -½ Q K* = w ½ r -½ Q L se = r ½ w -½ Q = (4/3)10 = 13.3 K se = w ½ r -½ Q = (3/4)10 = 7.5 TC at this L se & K se 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 Is MR still = MC? No. 36-2Q = 2w ½ r ½  36-2(10) < 2(3)(4) SE

Numerical Example of Long-run Input Demand What is the new  -max level of output? 36-2Q = 2(3)(4)  Q* new = 6 units K Labor 5 Q* = 10 20 7.5 13.38 4.5 ScE Q* new = 6 What is the cost-minimizing way to produce any level of Q? Recall L* = r ½ w -½ Q K* = w ½ r -½ Q L* = (4/3)6 = 8, K* = (3/4)6 = 4.5 Scale effect of a wage increase is to decrease production level (Q), which means the firm needs less K and less L. Effect L K Original 20 5 Subst Effect-6.7+2.5 Scale Effect-5.3-3.0 Final Point 8 4.5

Gross Complements or Substitutes For labor, the SE and the ScE reinforce one another  D-curve for labor is downward-sloping. That’s good. Price of Input j Quantity of Input j D0D0 Gross Complements Shock:  Price of Input i Wage Labor D 4 \$9 2013.38 D1D1 +2.5 -3.0 For capital, the SE and the ScE work in opposite directions. If we  Price of input i: SE > ScE  Gross Substitutes SE < ScE  Gross Complements (notice that blue and yellow make green, actually that was total coincidence )

Gross Complements or Substitutes More than 2 inputs –Categories of L & K, energy, raw materials/supplies Cost-minimizing condition still same: W skill /MP skill = W unskill /MP unskill = r/MP K 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) Price of Input j Quantity of Input j D0 Gross Substitutes Gross Complements Shock:  Price of Input i

Competitive Firm Example Assume firm operates in a perfectly competitive output market and perfectly competitive input markets Let Q = f(K,L) = K 1/3 L 1/3 Find unconditional factor demand functions and firm supply curve. Comparative statics

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