1 / 7

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.

ulmer
Download Presentation

Economics 202: Intermediate Microeconomic Theory

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related