Lecture 9 _Feb 16_ - Economics 100A Lecture #9: Tuesday,...

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
Economics 100A Lecture #9: Tuesday, Feb. 16 1) Cost minimization (§7.2) 2) Returns to scale (§6.5) 3) Technical progress (§6.6) 4) Cost concepts (§7.1)
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
(1) Cost minimization The firm’s problem: Find cheapest input combination that produces the desired output Why? Because failure to minimize cost will sacrifice some profits not profit maximizing Therefore, profit-max’ing firms want to solve: Minimize L,K Total Cost = rK + wL Subject to: f(L,K) = Q 0 “Constrained optimization” once again!
Background image of page 2
Cost min (cont’d) The parameters and constraints w = wage rate (e.g., $12 per hour for worker) r = rental rate of capital (e.g., $200 per hour for use of a backhoe)
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Iso-cost lines Input combinations that cost the same amount : wL + rK = TC (a constant) Solve for capital in terms of labor: K = (TC - wL) / r Slope of iso-cost line = Δ K/ Δ L = - w/r Compare with budget lines Budget line slope = -P X /P Y But a firm has no budget!! Intercepts: K = TC/r and L = TC/w
Background image of page 4
K , Units of capital per hour a b d e c $150 isocost $100 isocost $50 isocost $100 ——— $5 = 20 $150 ——— $5 = 30 $50 ——— $ 5 = 10 $100 ——— $10 10 = $50 ——— $10 5 = $150 ——— $10 15 = L , Units of labor per hour Family of iso-cost lines
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Iso-cost meets iso-quant Lowest iso-cost on a given iso-quant Slope of iso-quant = -MRTS L,K = - MP L /MP K Slope of iso-cost = w / r Put the two together: MRTS L,K = MP L /MP K = w / r Another view: MP L /w = MP K /r 1/w = amount of labor that can be purchased for $1 MP L = the amount of output that can be produced with last unit of labor MP L ×(1/w) = output derived from last $ spent on labor Similar interpretation for capital Equate incremental output of last $ spent on each input across inputs
Background image of page 6
L K TC 0 /w TC 1 /w TC 2 /w TC 2 /r TC 1 /r TC 0 /r Isoquant Q = Q 0 increase in cost decrease in cost Iso-cost meets iso-quant
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Extremes of technical substitution L K L K TC/w TC/r TC/w TC/r Perfect complements Perfect substitutes Q 0 Q 0
Background image of page 8
(2) Returns to scale When “scale up” all inputs, does output scale up same/more/less? Suppose that all inputs doubled … then
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 10
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 03/18/2010 for the course ECON 100A taught by Professor Woroch during the Spring '08 term at University of California, Berkeley.

Page1 / 33

Lecture 9 _Feb 16_ - Economics 100A Lecture #9: Tuesday,...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online