ECON 100A Midterm 2Review Session #2

Marquise McGrawHead GSI

November 4, 2012

Overview

• Mix of T/F, short-answer and mini-lectures on the most important topics.

• Focus is on graphs and intuition, not calculations and derivations.

• 2 hours (though we may go a bit over).• Brief time for Q&A at the end (up to 30 min).• Slides will be posted on bSpace afterward.

Structure

• Short-Run Cost and Production Decisions (35 min)

• Long-Run Cost and Production Decisions (35 min)

• Changes in Welfare due to Policy Interventions (30 min)

• Choice Under Uncertainty (15 min)

SHORT RUN PRODUCTION

SR Production with Variable Labor

Diminishing Marginal Product• If a firm keeps increasing an input, holding all other

inputs and technology constant, the corresponding increases in output will eventually becomes smaller.• Occurs at L=10 in previous graph

• Note that when MPL begins to fall, TP is still increasing

APL and MPL

• Moreover, diminishing marginal product implies that for some L>>0, marginal costs must be decreasing.

• Thus, beyond the optimum L*, where the crossing occurs, MPL must be greater than APL.

Short Run Cost Curves – Graphically

Effects of a $10 per unit tax on AC, MC curves.Note a lump-sum tax only moves ATC curve, not AVC or MC.

Short-Run Costs

• T/F (P9). Average fixed costs never increase as output increases.

• True. The definition of “fixed” costs are costs that are independent of output. As a result, AFC=FC/q can only decrease as q increases.

Short-Run Costs

• T/F The shape of the AC curve is independent of the diminishing marginal returns to labor.

• False. Shape of the AC curve is driven by diminishing marginal returns to labor in the AVC curve. This is because AVC=VC/q=wL/q=w/APL in the short run.

• Since we’ll need it for the next question,

Short Run Costs

T/F (P8). A firm with U-shaped short run average variable cost curve will never produce output where MPL > APL. • True. From the previous problem, we know that

AVC=w/APL, and MC=w/MPL. Rearranging gives APL=w/AVC and MPL = w/MC. Now if the premise of the problem is true, then w/MC > w/AVC, which in turn implies that MC<AVC. However, from the shutdown condition, we know MC>=AVC otherwise we don’t produce. Therefore, the premise of the problem is false, and the answer to the question asked is true.

SHORT RUN MARKET SUPPLY

Short-Run Market Supply (Identical Firms)

• The market supply curve is the horizontal sum of the firm supply curves.

Short-Run Market Supply (Different Firms or Plants)

• The market supply curve is the horizontal sum of the firm supply curves.

LONG RUN PRODUCTION

Long-Run Production

• Suppose that as long as neither input exceeds four times the other, capital and labor are perfect substitutes at a one-to-one ratio. However, once the input ratio reaches four to one in favor of either input, no further substitution is possible. Draw the isoquants.

• What is the elasticity of substitution over the part where K and L are substitutable?

Elasticity of Substitution

• Measures the ease with which we can substitute capital for labor.

• Tells us how the input factor ratio changes as the slope of the isoquant changes.

• If σ large, implies isoquant relatively flat. As σ decreases, “curviness” increases, implying that it is easier to substitute.

Answer

( / )

/1*

0 /

K L MRTS

MRTS K LMRTS

K L

Thus, these are infinitely substitutable, given the linear nature of the isoquant, from L=1 to 4. Beyond that, no substitutability is possible so sigma = 0.

Cobb-Douglas Expansion Path and Cost Minimization

• T/F: The long-run expansion path for the Cobb-Douglas function is horizontal.

• False: The LR output expansion path is a ray from the origin. We will show this mathematically using cost-minimization. This will also serve as a review of how to do a cost-minimization problem. (See board). We will also show that the SR EP is horizontal.

• ON YOUR OWN: Show that the output expansion path when the inputs are perfect substitutes is either a horizontal line or vertical line depending on w>r or w<r.

Cobb-Douglas Expansion Paths

http://www.economics.utoronto.ca/osborne/2x3/tutorial/OEPEX.HTM

How LR Cost Varies with Output• As a firm increases

output, the expansion path traces out the cost-minimizing combinations of inputs employed.

• We hold input cost constant, but vary the total output and cost.

• Cost minimization implies that we would have to change input prices but hold an isoquant constant to find the expansion path of output holding COST constant.

Long-Run

Factor Price Changes• Originally, w = $24 and r

= $8. When w falls to $8, the isocost becomes flatter and the firm substitutes toward labor, which is now relatively cheaper.• Firm can now

produce same q=100 more cheaply.

7.3 How LR Cost Varies with Output

• The expansion path enables construction of a LR cost curve that relates output to the least cost way of producing each level of output.

• Question: What would the LRMC=LRAC curve look like?

• Answer: Flat line at the LRMC amount of $2.

Shape of LR Cost Curves

• T/F The long-run average cost curve is U-shaped for the same reasons that the short-run average cost curve is U-shaped.

• FALSE – in SR U-shape due to downward sloping AFC or diminishing marginal returns. In LR this is due to economies and diseconomies of scale.

Shape of LR Cost Curves

• T/F: Since the LRAC is determined by the lower envelope of the AC curves, the LRMC is determined by the lower envelope of the MC curves.

• False. For any output level q > 0, the long-run marginal cost of production is the marginal cost of production for the short-run production levels chosen by the firm.

Short-Run & Long-Run Marginal Cost Curves

AC(q)

$/output unit

q

SRACs

Because a firm cannot vary K in the SR but it can in the LR, SR cost is as least as high as LR cost.• … and even higher if the “wrong” level of K is used in the SR.

Short-Run & Long-Run Marginal Cost Curves

AC(q)

$/output unit

q

SRMCs

Short-Run & Long-Run Marginal Cost Curves

AC(q)

MC(q)$/output unit

q

SRMCs

For each y > 0, the long-run MC equals theMC for the short-run chosen by the firm.

Returns-to-Scale and Av. Total Costs

y

$/output unit

constant r.t.s.

decreasing r.t.s.

increasing r.t.s.

AC(y)

Returns-to-Scale and Total Costs

• What does this imply for the shapes of total cost functions?

Returns-to-Scale and Total Costs

y

$c(y)

y’ 2y’

c(y’)

c(2y’) Slope = c(2y’)/2y’ = AC(2y’).

Slope = c(y’)/y’ = AC(y’).

Av. cost increases with y if the firm’stechnology exhibits decreasing r.t.s.

Returns-to-Scale and Total Costs

y

$c(y)

y’ 2y’

c(y’)

c(2y’)

Slope = c(2y’)/2y’ = AC(2y’).

Slope = c(y’)/y’ = AC(y’).

Av. cost decreases with y if the firm’stechnology exhibits increasing r.t.s.

Returns-to-Scale and Total Costs

y

$c(y)

y’ 2y’

c(y’)

c(2y’)=2c(y’)

Slope = c(2y’)/2y’ = 2c(y’)/2y’ = c(y’)/y’so AC(y’) = AC(2y’).

Av. cost is constant when the firm’stechnology exhibits constant r.t.s.

CRS and Long Run Suppy

• T/F If a firm has constant returns to scale production technology, then its long-run marginal cost curve is horizontal.

• True. This is because with constant returns to scale, the average cost remains constant as Q increases, so that it coincides with the marginal cost curve.

Returns to Scale• T/F If there is a single input to production and there are decreasing returns

to scale, then the marginal product of the input will be diminishing. • True, but only if there is only one input to production. In this case, say

labor is the only input. Then MC=w/MPL. So if MPL is decreasing, MC is increasing, which drives higher costs which leads to the increasing cost function that exhibits decreasing returns to scale.

• Note that if you had more than one input, this would be False. Note that there is no direct connection between returns to scale (increasing, constant, decreasing) and the rate change of the marginal product of an input! Returns to scale tells us how the output changes as all inputs change by the same factor; the marginal product concerns how output changes as one input changes, holding all other inputs fixed. In particular, a production function can have increasing returns to scale even though the marginal product of every input decreases as more of that input is used.

DEVIATIONS FROM PERFECTLY COMPETITIVE MARKETS - SUPPLY

38

Perfect Competition• A perfectly competitive industry is one that

obeys the following assumptions:– there are a large number of firms, each

producing the same homogeneous product– each firm attempts to maximize profits– each firm is a price taker• its actions have no effect on the market price

– information is perfect– transactions are costless

39

Short-Run Price Determination• The number of firms in an industry is fixed• These firms are able to adjust the quantity

they are producing– they can do this by altering the levels of the

variable inputs they employ

40

Short-Run Market Supply• The quantity of output supplied to the

entire market in the short run is the sum of the quantities supplied by each firm– the amount supplied by each firm depends on

price• The short-run market supply curve will be

upward-sloping because each firm’s short-run supply curve has a positive slope

Long-Run Market Supply Curve (Summary)

• Scenarios in which LR market supply is not flat:1. LR market supply when entry is limited• Upward-sloping if government restricts number of firms, firms need a

scarce resource, or if entry is costly LR market supply when firms differ

• Upward-sloping if firms with relatively low minimum LRAC are willing to enter market at lower prices than others

2. LR market supply when input prices vary with output• In an increasing-cost market input prices rise with output and LR market

supply is upward-sloping• In a decreasing-cost market input prices fall with output and LR market

supply is downward-sloping3. Firms differ in their long-run cost structures

8.4 Long-Run Market Supply Curve

• Identical firms, free entry into the market, and constant input prices.

Limited Entry• Restricting the

number of firms causes supply to shift left

LR Supply when Firms Differ in Cost Structures

Long-Run Market Supply Curve: Increasing-Cost Market

POLICY INTERVENTIONS AND EFFECTS

47

Taxes• Creates revenue for

government to spend, decreases consumer and producer surplus, results in deadweight loss

Taxes

• For a given tax, if the government wants to maximize tax revenues it should tax a good with a relatively inelastic demand.

• TRUE. This minimizes the area of the DWL triangle. Draw a picture to convince yourself.

49

Tax burden and elasticity - summary

Tax burden on each is determined by the elasticities of supply and

demand.

Given the demand curve, more elastic (flatter) supply means

greater tax burden for consumers.

Given the supply curve, more elastic (flatter) demand means greater tax burden for sellers.

Supply and Demand and Market Efficiency

Figure 4.9(a) shows the consequences of producing 4 million hamburgers per month instead of 7 million hamburgers per month. Total producer and consumer surplus is reduced by the area of triangle ABC shaded in yellow. This is called the deadweight loss from underproduction. Figure 4.9(b) shows the consequences of producing 10 million hamburgers per month instead of 7 million hamburgers per month. As production increases from 7 million to 10 million hamburgers, the full cost of production rises above consumers’ willingness to pay, resulting in a deadweight loss equal to the area of triangle ABC.

50

Policies That Create a Wedge Between Supply and Demand Curves

• Price floor creates wedge that generates excess production of Qs – Qd and DWL of C+F+G.

9.5 Policies That Create a Wedge Between Supply and Demand Curves

• Price ceiling creates wedge that generates excess demand of Qd – Qs and DWL of C+E.

9.4 Free Trade vs. No Trade• With free trade, domestic

producers supply Q=8.2 and imports of Q=4.9 fill out our additional demand for oil at the low world price.

• With no trade, we lose surplus equal to area C.• This is the DWL of a

total ban on trade.

9.4 Tariffs• A tariff is essentially a tax on imports and there are two common

types:• Specific tariff is a per unit tax• Ad valorem tariff is a percent of the sales price

• Assuming the U.S. government institutes a tariff on foreign crude oil:

1. Tariffs protect American producers of crude oil from foreign competition.

2. Tariffs also distort American consumers’ consumption by inflating the price of crude oil.

9.4 Tariffs• A $5 per unit (specific) tariff

raises the world price, which increases the quantity supplied domestically and decreases the quantity imported.

• Tariff revenue of area D is generated by the U.S.

• DWL is equal to C+E.

9.4 Quotas• A quota is a restriction on the amount of a good that can be

imported.• When analyzed graphically, a quota looks very similar to a tariff.

• A tariff is a restriction on price• A quota is a restriction on quantity• One can find a tariff and a quota that generate the same

equilibrium• The only difference is that quotas do not generate any additional

revenue for the domestic government.

9.4 Quotas• An import quota of 2.8

millions of barrels of oil per day increases the quantity supplied domestically and decreases the quantity imported.• Equivalent to $5 per unit

tariff• DWL is equal to C+D+E

because no tariff revenue is generated.

Practice Question – Tariffs/QuotasThe domestic demand for portable radios is given by Q=5000-100P. The supply curve is given by Q=150P. (Q is in thousands, P is in dollars)

a) What is the domestic equilibrium in the market?b) Suppose portable radios can be imported at a world price of $10 per radio.

If the trade were unencumbered, what would the new market equilibrium be? How many portable radios would be imported?

c) If domestic portable radio producers succeed in getting a $5 tariff implemented, how would this change the market equilibrium? How much would be collected in tariff revenues? How much consumer surplus would be transferred to domestic producers? What would the deadweight loss from the tariff be?

d) How would your results from part c be changed if the government reached an agreement with foreign suppliers to voluntarily limit the portable radios they export to 1,250 a year? Explain how this differs from the case of a tariff.

CHOICE UNDER UNCERTAINTY

Risk Premium

• T/F The risk premium of a risk preferring individual is zero.

• False. See next slide.

61

Why do people gamble if they know they will lose money?

•Increasing MU of money (depicted by utility function above), OR•Diminishing MU with EU<U(Y*) but person is wiling to pay the difference in order to get that thrill

62

Risk under Uncertainty

Give:a) The expected wealth of the

homeowner.B) The homeowner’s expected utility.C) Minimum price an insurance

company would charge for an insurance policy.

D) How much better off would the homeowner be with the insurance policy (in terms of utility)?

E) Would the homeowner pay $600,000 to be guaranteed wealth of 1.4 million? Why?

A homeowner is subject to the following risky situation. If there are no fires, the house has a value of $2 million. If there is a fire, the homeowner is only left with the land, which has a value of $1 million. There is a 50% chance of a fire. The homeowner’s utility is shown in the graph below.

63

Insurance (2009 Final, Q4b)

A B C

Last Things

• Thanks for coming and good luck!• You can leave now, or stay for the brief Q &A. • No more questions after 30 minutes from

now.• Office Hours: Monday 1-2:30 542 Evans • NO EMAILS PLEASE.