Cost Benefit Analysis Example Modified

8/10/2019 Cost Benefit Analysis Example Modified

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We are going to do a complete cost benefit analysis of atariff on steel by the US government.

As explained in the last set of slides, we are going touse a table to make sure that we have accounted foreverything.

We will complete a series of 5 tables.

The following is the basic information we need tocomplete the tables.


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Before In the beginning the US does not have a tariff on steel.

Since there is no tariff, the US price of steel is the same

as the world price of steel. Say the price of steel was $9 per pound.

At $9 per pound, US users of steel bought 60 poundsof steel.

Where did these 60 pounds come from? 10 pounds were supplied by US producer of steel.

50 pounds were imported.


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After Now the US imposes a $5 per pound tax on imported

steel.

Because of the tariff, the US price of steel (inclusive ofthe $5 tariff) is going to be different from the worldprice of steel (exclusive of the tariff).


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What will be the world price of steel (exclusive of thetariff)? Will it remain at $9 per pound?

Potential pitfall number 6 reminds you not to assume

things to stay the same. If the US is a large buyer of steel, it is unlikely that theworld price of steel will remain at $9?

Is it going to go up or go down? It will go down. This is because the $5 tariff reduces the

demand for imported steel. When demand goes down,price goes down. (Just like when we dont demand cordedphones, the price of corded phone drops.)

Assume that it goes down to $8. So the new world price of steel is $8 exclusive of the tariff.


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What will be the US price of steel inclusive of thetariff?

It will be equal to the $8 world price of steel plus the $5tariff.

So the US price of steel (inclusive of the tariff) will be$13.


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How much will US users of steel buy? Will theycontinue to buy 60 pounds of steel?

No, US price of steel is now higher at $13 instead of $9.When price is higher, people buy less.

So US users of steel will buy less.

Assume that US users will now buy 55 pounds at $13

per pound. So US users will cut back on steel use by 5 pounds (60

minus 55) due to the tariff.


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So when there is a tariff, US users will buy 55 pounds ofsteel?

Where do these 55 pounds come from?

Will US producers continue to supply 10 pounds?

No, US price is higher at $13 instead of at $9 so USproducers will supply more at the higher price.

Assume that US producers will now supply 25 pounds atthe higher price of $13 (compared to 10 pounds at the lowerprice of $9).

The remaining 30 pounds (55 minus 25) will be imported.


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The following table sums up all the

information we need.BeforeNo tariff on steel

After$5 per pound tariff on steel

US users bought 60 pounds Now they buy 55 pounds. They buy 5

pounds less than before.US producers supplied 10 pounds Now they supply 25 pounds. They

supply 15 pounds more than before.

Import is 50 pounds (60 minus 10) Import is 30 pounds (55 minus 25)

World price of steel was $9 World price of steel is $8

US price of steel was $9 US price of steel (inclusive of tariff) is$13


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To avoid potential pitfall number 2, we will account forall quantities by fully accounting for the 60 poundsoriginally bought by US users before the tariff.


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60 pounds bought by US users when there was no tariff

Table 110 pounds suppliedby US producers

50 pounds imported whenthere was no tariff

Table 2Additional 15pounds nowsupplied by US

producers whenthere is a tariff

Table 330 poundsimported whenthere is a tariff

Table 4US users cut backby 5 pounds whenthere is a tariff


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Table 1The 10 pounds of steel supplied by US producers both before and after the

tariff

Before After Gain(after minus before)

Loss(after minus before)

Net effect(+ is netgain; - is netloss)

US producers Sold at $9per pound

Sold at $13per pound

$4 more per poundtimes 10 pounds =$40 more in revenue

No change in thecost of producingthese 10 pounds

+$40

US users Bought at$9 perpound

Bought at$13 perpound

No change in valuefrom these 10pounds

$4 more per poundtimes 10 pounds =$40 more in expense

-$40

US govt Not

involved

Not

involved

0 0 0

US as a whole 0


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Table 2The 15 pounds increase in production by US producers due to the tariff



Net effect(+ is net

gain; - is netloss)

US producers Notproduced

Sold at $13per pound

$13 per pound times15 pounds = $195more in revenue

$11 per pound times15 pounds = $165more in cost. SeeBox A explanation.

+ $30

US users Bought at$9 perpoundfromabroad

Bought at$13 perpoundfrom USproducers



-$60

US govt Notinvolvedbecausethere wasno tariff

Notinvolvedbecausethese 15pounds arenotimports

0 0 0

US as a whole - $30See Box Bexplanation


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Box A explanation The loss in Box A is the cost of producing 15 pounds of

steel.

Do we know the cost of producing 15 pounds of steel?We dont know the exact cost.

However, we can form a reasonable estimate based ontwo observations.


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Box A explanation continued Observation 1:

US producers are producing and selling 15 pounds

more of steel when the price is higher at $13 after thetariff.

Observation 2:

US producers were not producing and selling these 15

pounds of steel when the price was lower at $9 beforethe tariff.


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US producers are producing and selling 15 pounds

more of steel when the price is higher at $13 per poundafter the tariff.

What does this tell you about the maximum (average)cost of producing 1 pound of steel?

The (average) cost is at most $13.


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US producers were notproducing and selling these 15

pounds of steel when the price was lower at $9perpound before the tariff.

What does this tell you about the minimum (average)cost of producing 1 pound of steel?

The (average) cost is at least $9.


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Box A explanation continued So the maximum average cost is $13.

And the minimum average cost is $9.

A reasonable estimate of the average cost is the middlebetween the maximum and the minimum.

Therefore ($13 + $9) divided by 2 = $11 is a reasonableestimate of the average cost.

The total cost of producing 15 pounds is then $11 times15 = $165, which is in Box A.


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Box B explanation In Box B we see that the US as a whole has a loss of $30. Here is an intuitive explanation of this loss. Before the tariff, the US was paying $9per pound to import

these 15 pounds of steel from abroad. After the tariff, the US was producing these 15 pounds of

steel at home at an average cost of $11. So the US is paying $2 more per pound ($11 minus $9). $2 more per pound times 15 pounds is $30.

This explanation is intuitive and is a short-cut. There is still value in doing the long table. We are sure that

we have accounted for everything and that we have not leftanything out.


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Box B explanation continued The technical name for the $30 loss in Box B is:

Change in producer surplus.

It is also called the deadweight loss due to productiondistortion.

With a tariff, the US is over-producing steel by 15pounds. Those 15 pounds should have been imported

at $9 per pounds instead of being produced at home at$11 per pounds. We call this over-production aproduction distortion.


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Box B explanation continued The $30 loss can also be calculated as the area of a (right-

angle) triangle.

The base is the increase in US production of steel due tothe tariff.

The height is the increase in US price of steel due to thetariff (from $9 to $13).

The area of this triangle is base times height divided by 2 =15 times 4 divided by 2 = 30

So the deadweight loss is also called a deadweight losstriangle.

Base is15 pounds

Height is$4


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Table 3The 30 pounds of steel imported by the US after the tariff



Net effect(+ is net

gain; - is netloss)

US producers Notinvolved

Notinvolved

0 0 0

US users Bought at$9 perpoundfromabroad

Bought at$13 perpoundfromabroad



-$120

US govt Notinvolved

becausethere wasno tariff

$5 perpound

tariff

$5 per pound tariffrevenue times 30

pounds = $150increase in tariffrevenue

0 +$150

US as a whole + $30


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Note that from Table 3, the US government collects$150 of tariff revenue.

However, these $150 does not represent a net gain tothe US from the 30 pounds of steel import.

This is because US users pay $120 more for these 30pounds of steel than before the tariff.

So the net gain to the US from these 30 pounds is $30($150 gain to US government minus $120 loss to USusers).


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Table 4The 5 pounds decrease in purchase by US users of steel when price went

from $9 to $13 per pound due to the tariff



Net effect(+ is netgain; - is netloss)

US producers Notinvolved

Notinvolved

0 0 0

US users Bought at$9 per

pound

Not boughtat $13 per

pound

Expenditure wentdown by $9 per

pound. Total savingis $9 time 5 = $45

Lose $11 in value perpound for 5 pounds.

Total is $11 times 5 =$55. See Box Cexplanation.

+ $45 - $55 =- $10

US govt Notinvolvedbecausethere was

no tariff

Notinvolvedbecausethese 5

pounds areno longerimported

0 0 0

US as a whole - $10See Box Dexplanation.


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Box C explanation US users of steel cut back on their purchase of steel by

5 pounds when the price went up from $9 to $13 due tothe tariff.

When they do not buy these 5 pounds, users lose thevalue that could be obtained from steel. For example,the user could have used the steel to build a ship andsell the ship for a profit.

How much value do users lose?

We dont know the exactvalue.

However, we can form a reasonable estimate based ontwo observations.


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Box C explanation continued Observation 3:

US users are not buying these 5 pounds when the priceis higher at $13 after the tariff.

Observation 4:

US producers were buying these 5 pounds of steelwhen the price was lower at $9 before the tariff.


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US users are not buying these 5 pounds when theprice is higher at $13 after the tariff. What does this tellyou about the maximum (average) value of steel?

The (average) value is at most $13.


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US producerswere buying these 5 pounds of steelwhen the price was lower at $9before the tariff.

What does this tell you about the minimum (average)value of 1 pound of steel?

The (average) value is at least $9.


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Box C explanation continued So the maximum average value is $13.

And the minimum average value is $9.

A reasonable estimate of the average value is themiddle between the maximum and the minimum.

Therefore ($13 + $9) divided by 2 = $11 is a reasonableestimate of the average value.

The total value of 5 pounds is then $11 times 5 = $55,which is in Box C.


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Box D explanation In Box D we see that the US as a whole has a loss of $10.

Here is an intuitive explanation of this loss. Before the tariff, the US was buying steel at $9 per pound but the

value is estimated to be $11 per pound.

After the tariff, the US is not buying those 5 pounds. The US is

no longer paying $9 per pound so that is a saving. However, sincewe are not buying the steel, we also lose the $11 value from steel.

So the net loss to the US is $2 per pound ($11 value we are notgetting minus the $9 saving).

$2 per pound times 5 pounds is $10.

This explanation is intuitive and is a short-cut.

There is still value in doing the long table. We are sure that wehave accounted for everything and that we have not left anythingout.


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Box D explanation continued The technical name for the $10 loss in Box D is:

Change in consumer surplus.

It is also called the deadweight loss due toconsumption distortion.

With a tariff, the US is under-using steel by 5 pounds.Those 5 pounds should have been imported at $9 per

pounds to generate $11 per pound in value. We call thisunder-consumption a consumption distortion.


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Box D explanation continued The $10 loss can also be calculated as the area of a (right-

angle) triangle.

The base is the decrease in US usage of steel due to thetariff.

The height is the increase in US price of steel due to thetariff (from $9 to $13).

The area of this triangle is base times height divided by 2 =5 times 4 divided by 2 = 10

So the deadweight loss is also called a deadweight losstriangle.

Base is 5 pounds

Height is$4


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Now we can put the four tables together to get anoverall net gain/loss to the US as a whole.

Table 5Overall Net Effect on US as a Whole

Table 1 0

Table 2 -$30

Table 3 +$30

Table 4 -$10

Overall net effect of a tariff -$10


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So in this example, the overall net effect on the US is a lossof $10. In this case, the tariff is bad for the US as a whole.

However, this will not always be the case.

Note that Table 1 will always show no gain or loss. Table 2 and 4 will always show a loss. That is why they are

called deadweight losses you cannot avoid them as longas there is a tariff.

The only gain comes from Table 3. If the gain in Table 3 islarge enough, it can offset the deadweight losses in Tables 2and 4. If the gain in Table 3 is small, a tariff will result in anoverall net loss to the US as a whole.

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Cost Benefit Analysis Example Modified

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