lecture 13 econ 100a kamala

8/11/2019 Lecture 13 Econ 100A Kamala

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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

lecture 13 econ 100a kamala

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