# ECON 2X03 Lecture Notes - Lecture 2: Isocost, Zirconium, Bzip2

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Published on 18 Apr 2013

Department

Economics

Course

ECON 2X03

Professor

Lecture 2

Long Run Cost Minimization

- Long run: all inputs variable

- Cost minimization: selecting quantities of the inputs to minimize costs given a particular output

- Zi = input i

- Y = output

- Wi = cost per unit of input i

- Min(z1,z2) w1z1 +w2z2

o Subject to F(z1,z2) = y

- Consider firms with diminishing MRTS:

o Assume that from the firm;s perspective, the cost per unit of inputs is fixed, the cost (c)

of some input bundle is C = w1z1 + w2z2

o Isocost: a line along which the input bundles have the same cost (FIXED)

o C = w1z1 + w2z2

o Z2 = c/w2 + w1*z1/w2

o Cost-min where:

slope of isoquant = slope of isocost

MRTS = w1/w2

- MP1 = Δy/ Δz1 Δz1 = Δy1/MP1

- MP2 = Δy/ Δz2 Δz2 = Δy2/MP2

- MRTS = -Δz2/Δz1 = (-Δy2/MP2)/( Δy1/MP1)

- MRTS = (-Δy2/MP2)*(MP1/Δy) = -

(Δy2/Δy1)*(MP1/MP2)

- Since Δy2 = -Δy1 ( since back to same isoquant):

o MRTS = MP1/MP2

With diminishing MRTS:

- Cost-min condition is MP1/MP2 = w1/w2