lecture 13 econ 100a kamala
TRANSCRIPT
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Econ 100AMicroeconomic Analysis
Lecture 12: Reading: Chapter 6, 7
1
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Recap
Short-run production:
Total product curve
Marginal productivity of labor
Average productivity of labor
LR/SR Expansion path
Returns to scale
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Question #26
When APL is downward sloping, MPL is
negative
A. True
B. False
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Question #27
If the production function is linear then APL=
MPL
A. True
B. False
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Recap
Long-run production:
Isoquants & isocost
Lagrangian method to minimize costs
MRTS
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Cost minimizationthe math
Setting up the Lagrangian:
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Example
Let q = (sqrt(L) + sqrt(K))2
Find the optimal quantity of K as a function of
L (expansion path equation!!!)
Given w = 8 and r = 4, find the optimal level of
capital and labor to produce 64 units
Find total expenditure
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From production to costs
Chapter 7: 7.1-7.4
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From production to costs
Production function tells us how much quantityis being produced for different levels of labor
and capital
Cost function tells us how much production
costs as a function of quantity produced
TC = g(Q) = g(f(K,L))
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Total Costs
Total costs include the cost of labor and capital
Capital costs are the rental costs of capital
The rental rate, r, is the opportunity cost of capital
The cost of labor is the hourly wage, w
TC = wL + rK
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Short-run costs
Let production function be: Q = 2LK2
Let K = 2, r = 10
w = 8
Write Labor as a function of quantity:
Find total costs as a function of Q: TC = wL +rK
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Fixed Costs
Do not change with quantity produced.
Need to pay them even if production = 0
Can be eliminated only if shut-down
The costs associated with capital (the fixed input)
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Variable Costs
Vary with output level.
Can be eliminated by stopping production
The costs of labor (the variable input)
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Example
TC = 125 + 20Q - 5Q2+0.5Q3
ATC = TC/Q =
FC =
AFC = FC/Q =
VC =
AVC = VC/Q =
MC = dTC/dQ =
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MC, AVC, ATC
MC decreases then increases
Goes through the minimum of AVC and ATC
Can you show with math? Derive TC/Q w.r.t Q
and find when it equals zero.
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Question #28
An increase in the rental costs of capital willnot change the following curve
A. ATC
B. MC
C. AFC
D. TC
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Why is the Short-run AC curve U-shaped?
AC initially decreases because of average Fixed
Costs
When diminishing marginal product of labor
kicks in, MC start to increase, pushing AC up
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Marginal Cost and Marginal Productivity
In the SR, variable cost is the wage times the
additional labor hired
VC = wL
Therefore:
MC = VC/Q = wL /Q = w/MPL
The cost of the last unit produced is wage over
marginal productivity of labor
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Cobb-Douglas Short-run costs
i. Let production function be: Q = L
K1-
ii. Let K = K, r and w are exogenous
i. Find the expression for total costs ($ as a function
of Q)
ii. Find marginal costs
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Long-run costs
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RTS & CostsK L TC Q AC
10 10 1000 100
20 20 2000 400
40 40 4000 1000
K L TC Q AC
10 10 1000 100
20 20 2000 150
40 40 4000 180
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Returns to Scale and LR costs
IRTS: Average Costs decrease as output
increases
CRTS: Average Costs are constant as outputincreases
DRTS: Average Costs increase as output
increases
Assumes w,r fixed!!!
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LR Cost Curves
CRTS IRTS DRTS
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The U-Shaped Long Run Cost Curve
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SR vs. LR costs - Example
Mokia, a new cell phone company, makescellular phones designed especially for coffee
lovers. The production function is given by
q(K,L) = L1/2*K1/3. Cost of labor is $9 per hour
and rental cost of capital is $4.
Does this function exhibit I/D/C RTS?
Find the expansion path equation
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Example
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Example
Mokias first order is for 72 phones. How many
labor hours do they employ? How much capital
do they use?
What are TC?
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Example
Peets coffee decided to offer a promotional deal
for Mokia phones in their store. The next day
Mokias order was for 600 phones. Assuming
they want to provide the phones to their
customers ASAP, how many units of labor will
they use?
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Example
What would be costs associated with short-runproduction of 600 phones?
What would be costs associated with long-runproduction of 600 phones?
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Question #29
The MC of a firm with IRTS is always smallerthan the AC
A. True
B. False