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nycgrrl012 nycgrrl012
wrote...
Posts: 4
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A year ago
The demand and supply curves for bricks are given by

P = 100 - Q/2

and

P = 2Q

respectively.

The government, fearful that a bricks have shortage could jeopardize national security, imposes a tax of $20/oz. on the retail price of this rare metal. It collects the tax from bricks sellers. What is the equilibrium quantity in the market? What is the price paid by the buyer? The price received by the seller net of the tax?

I do not understand the equations, how to manipulate then, and how I end with the tax. Can someone please show the work?

Is Q = 40?
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Anonymous
wrote...
A year ago
To find the equilibrium quantity and price, we need to set the demand and supply curves equal to each other and solve for Q and P:

100 - Q/2 = 2Q

Multiplying both sides by 2, we get:

200 - Q = 4Q

5Q = 200

Q = 40

Substituting Q = 40 into either the demand or supply equation, we get:

P = 2Q = 2(40) = 80

So the equilibrium quantity is 40 and the equilibrium price is $80.

Now we need to add the tax. The tax of $20/oz. is collected from the sellers, so they will have to pay an additional $20/oz. on top of their cost. This means that the new supply curve is:

P = 2Q + 20

To find the new equilibrium, we set the new demand and supply curves equal to each other:

100 - Q/2 = 2Q + 20

Multiplying both sides by 2, we get:

200 - Q = 4Q + 40

5Q = 160

Q = 32

Substituting Q = 32 into the supply curve, we get:

P = 2Q + 20 = 2(32) + 20 = 84

So the new equilibrium quantity is 32 and the new equilibrium price is $84.

The price paid by the buyer is $84, which includes the $20 tax paid by the seller. The price received by the seller net of the tax is $64, which is the original equilibrium price of $80 minus the $20 tax.
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