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April 23rd, 2017, 07:13 PM   #1
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Micro-economics

Hello

Can you help me please about the following exercise:

Demand function is Q = 400 - P
Supply function is Q = 3P

How much of tax for per unit of product should be set for make that the quantity will be reduced by x2? (x is a multiplication).

My answer is :
400 - P = 3P
P = 100

--------------------------
400 - P = 3P
400 - P = 0.5*3P
P = 160

--------------------------
The tax is: 160 - 160 = 100

I am not sure about my answer.

Thanks!
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April 24th, 2017, 03:57 AM   #2
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Quote:
Originally Posted by IlanSherer View Post
Hello

Can you help me please about the following exercise:

Demand function is Q = 400 - P
Supply function is Q = 3P

I am following up to here.


How much of tax for per unit of product should be set for make that the quantity will be reduced by x2? (x is a multiplication).

This sentence makes no sense at all. I am guessing that the quantity to be reduced is the quantity that would be exchanged in the absence of the tax. But if that guess is correct, that quantity could not be reduced by two times itself, thereby giving a negative quantity exchanged subject to the tax.

My answer is :
400 - P = 3P
P = 100

--------------------------
400 - P = 3P
400 - P = 0.5*3P
P = 160

--------------------------
The tax is: 160 - 160 = 100

I am not sure about my answer.

I am quite sure that $ 160 - 160 = 0 \ne 100.$

Thanks!
If I am correct that the question asks you to find the tax per unit sold that reduces the quantity sold by some factor (perhaps by 1/2), your first task is to determine what the quantity sold would be without the tax.

What is that quantity?

Now we get to the point of the exercise. What concerns the seller is what she gets EXCLUDING the tax because the tax goes to the state, not the seller. What concerns the buyer is what he pays INCLUDING the tax because both the amount received by the seller and the amount received by the state come out of the buyer's pocket. Understand that?

Can you set up the second part of the problem now?

Last edited by JeffM1; April 24th, 2017 at 04:01 AM.
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April 24th, 2017, 10:24 AM   #3
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Quote:
Originally Posted by JeffM1 View Post
If I am correct that the question asks you to find the tax per unit sold that reduces the quantity sold by some factor (perhaps by 1/2), your first task is to determine what the quantity sold would be without the tax.

What is that quantity?

Now we get to the point of the exercise. What concerns the seller is what she gets EXCLUDING the tax because the tax goes to the state, not the seller. What concerns the buyer is what he pays INCLUDING the tax because both the amount received by the seller and the amount received by the state come out of the buyer's pocket. Understand that?

Can you set up the second part of the problem now?
Yes, you right (by quantity*0.5 if you understand me)
I think i got you:

400 - P = 3P
P = 100
Q = 3P = 3*100 = 300

------------------------------
Q = 0.5*300 = 150
------------------------------
Q = 3P
150 = 3P
P = 50

The tax is: 100 - 50 = 50

Did i understand you?

Edit: or 0.5*P = 0.5*100 = 50

I'm confused.

Last edited by IlanSherer; April 24th, 2017 at 10:47 AM.
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April 24th, 2017, 11:18 AM   #4
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Without tax, clearing occurs where

$3p = 400 - p \implies p = 100 \text { and } q = 300.$

If the tax reduces sales to 0.5 * 300 = 150

then the price received by the seller must equal

$3p = 150 \implies p = 50$

and the price paid by the buyer must equal

$400 - p = 150 \implies p = 250.$

So the tax is $250 - 50 = 200 \ne 50.$

Why is your answer of 50 wrong? If the buyers must pay 100 but the government takes 50, the suppliers will provide only 150 units as you saw, but the buyers will still demand 300. No equilibrium. If the buyers must pay 150 and the government takes 50, the suppliers will get 100 and still supply 300, but the buyers will demand only 250. No equilibrium.

If the buyers pay 250, they will buy only 400 - 250 = 150.

If the sellers receive 50, they will supply 3 * 50 = 150. Equilibrium.

Notice that the tax of 200 is borne as follows: sellers get 50 less and the buyers pay 150 more.
Thanks from IlanSherer
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April 24th, 2017, 11:51 AM   #5
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Quote:
Originally Posted by JeffM1 View Post
Without tax, clearing occurs where

$3p = 400 - p \implies p = 100 \text { and } q = 300.$

If the tax reduces sales to 0.5 * 300 = 150

then the price received by the seller must equal

$3p = 150 \implies p = 50$

and the price paid by the buyer must equal

$400 - p = 150 \implies p = 250.$

So the tax is $250 - 50 = 200 \ne 50.$

Why is your answer of 50 wrong? If the buyers must pay 100 but the government takes 50, the suppliers will provide only 150 units as you saw, but the buyers will still demand 300. No equilibrium. If the buyers must pay 150 and the government takes 50, the suppliers will get 100 and still supply 300, but the buyers will demand only 250. No equilibrium.

If the buyers pay 250, they will buy only 400 - 250 = 150.

If the sellers receive 50, they will supply 3 * 50 = 150. Equilibrium.

Notice that the tax of 200 is borne as follows: sellers get 50 less and the buyers pay 150 more.
Jeff, you made me understand better, thanks a lot!
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