Macroeconomic Policy in the Global Economy Issue Paper
zack1011
ITRN503_2020-Spring_session-03_Ideas-and-Investment.pdf
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ITRN 503: Investment and Macroeconomics Auerswald
Professor Philip Auerswald
Session No. 3:
Ideas and Investment
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ITRN 503: Investment and Macroeconomics Auerswald
Session #32
Outline
• Introduction to Production Theory • Returns to Scale • Aggregate Production Function • Solow Paper
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Introduction to Production Theory
• What does the firm act to maximize? Profits. Specifically profits = total revenues - total economic costs
P = TR - TC • How do we represent the state of technology? By a production
function. output = y = f(k, l)
k = capital; l = labor Observations – What is missing from the production function above? The
recipe used to transform inputs into outputs. (More on this later.)
– What of the role of the entrepreneur in bring together unique combinations? The entrepreneur is subsumed into capital.
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Session #34
The Production Function
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Session #35
Isoquants of the Production Function q = q(k, l)= k0.5 l0.5
(Cobb-Douglas)
input k input l
3D plot of q(k, l) highlighting isoquants
ou tp
ut q
dq
dl
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ITRN 503: Investment and Macroeconomics Auerswald
Session #36
Marginal Rate of Technical Substitution (Between Two Inputs)y = f(k, l)= k0.5 l0.5
(Cobb-Douglas)
in pu
t k
input l
2D contour lines of of f(k, l) ® production isoquants
dk
dl
marginal rate of technical substitution=
-dk/dl
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ITRN 503: Investment and Macroeconomics Auerswald
Session #37
Isoquants of the Production Function q = q(k, l)= k0.5 l0.5
(Cobb-Douglas)
input k input l
3D plot of q(k, l) highlighting isoquants
ou tp
ut q
dq
dl dk
dl
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ITRN 503: Investment and Macroeconomics Auerswald
Cobb-Douglas Production Function
Session #38
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Cobb-Douglas Production Function
Session #39
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Session #310
Cobb-Douglas Production Function
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Elasticity of Substitution
Session #311
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Linear production function: q = k + l
σ = 1 Example? Economic meaning?
capital (k)
labor (k)
Infinite elasticity of substitution
Isoquants of the Production Function
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Session #313
σ = a constant
Example? Economic meaning?
capital (k)
labor (k)
=1 Cobb-Douglas production function
Elasticity of substitution = 1
Isoquants of the Production Function
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Session #314
Leontief production function: q = min[k,l]
σ = 0
Example? Economic meaning? Historical significance?
capital (k)
labor (k)
Elasticity of substitution = 0
Isoquants of the Production Function
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Session #315
• Graph: Pick the best possible Cost line, with production isoquant fixed (that is, production q held constant).
Minimizing the Cost of Producing a Given Quantity
quantity of kapital
quantity of labor
Cmin/w
Cmin/r
Ctoo much/r
Ctoo much/w
one point in the factor demand function
l* (w , r , q )
hold production at this level q
–
—
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Profit Maximization
Session #316
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Session #317
Profit Maximization
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Returns to Scale
Session #318
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Session #319
units quantity (q) –Note:r and w held constant
$/unit
marginal cost curve
¶C*(r,w,q)/ ¶q––
Constant Returns to Scale
Note: “Replication” argument for constant returns.
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Session #320
Note:r and w held constant
units quantity (q) –
marginal cost curve
¶C*(r,w,q)/ ¶q ––
$/unit
Decreasing Returns to Scale
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Session #321
Note:r and w held constant
units quantity (q) –
$/unit
marginal cost curve
¶C*(r,w,q)/ ¶q––
Increasing Returns to Scale
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Aggregate Production Function (Solow 1956)
Session #322
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Aggregate Production Function (Solow 1956)
Session #323
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ITRN 503: Investment and Macroeconomics Auerswald
Aggregate Production Function (Solow 1956)
Session #324
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Session #325
Cobb-Douglas Production Function
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Aggregate Production Function (Solow 1956)
Session #326
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Aggregate Production Function (Solow 1956)
Session #327
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Aggregate Production Function (Solow 1956)
Session #328
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Aggregate Production Function (Solow 1956)
Session #329
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ITRN 503: Investment and Macroeconomics Auerswald
Aggregate Production Function (Solow 1956)
Session #330
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Aggregate Production Function (Solow 1956)
Session #331
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Session #332
Q: Where does Solow get this?
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Session #333
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Session #334
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Session #335
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ITRN 503: Investment and Macroeconomics Auerswald
Session #336
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Session #337
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ITRN 503: Investment and Macroeconomics Auerswald
Session #338
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Session #339
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ITRN 503: Investment and Macroeconomics Auerswald
Session #340
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