Consider a market for beer with a demand curve which is:

Qd = 25 - 2p

and a supply curve which is:

Qs = 3P

If we wished to know **how to find the equilibrium quantity and price **all we would do is equate the supply equation and the demand equation such that:

Qd = Qs

25 - 2p = 3P

25 = 5P

5 = P

We can now substitute our price into either the supply or demand equation. I proceed by substituting it into the supply.

Q = 3(5)

Q = 15

Now suppose that the government decided they wished to levy a $2 tax on suppliers. We could re-write our price as follows:

P* = P - t

where

P = the market price

P* = the price suppliers receive

t = the tax they pay

thus

P* = P - 2

We know need to re-write our supply equation to incorporate the tax. Thus we would get:

Qs = 3(P-2)

Qs = 3P - 6

Now we can again equate supply equal to demand such that:

25 - 2P = 3P - 6

31 = 5P

P = 6.2

Which is what we expected since you assume that taxes will increase prices. We can now substitute this back into the supply and demand equation. This time I will put it into the demand equation as it will make things simpler as we will not need to worry about the tax.

Q = 25 - 2(6.2)

Q = 25 - 12.4

Q = 12.6

Thus we can see that the tax has made the market price increase, the quantity being produced decrease and the price suppliers receive decrease.

Finally we could simply calculate how much tax revenue that the government collects by multiplying the quantity produced by the tax rate.

Thus the tax revenue is:

Tax Revnue (TR) = Q * t

= 12.6 * 2

= 25.2

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