Suppose we have the following system of equations:
$Q_s=-20+3P$
$Q_d=-220-5P$
$Q_s=Q_d$
Say we want to find the tax burden of the consumer, the tax burden of the firm, and the total revenue generated for the government for some excise tax t.
Do we do this by looking at the elasticity of each the supplier and consumer?
The Elasticity of Q with respect to P can be calculated by:
$\eta_Q,_P = P/Q*dQ/dP$
With this we see that the elasticity of supply is 3 and the elasticity of demand is -5
Can we use these to find the tax burden? And how do we calculate the government tax revenue in terms of t for the government?
Best Answer
You've got three equations: $$(1)Q_s=-20+3P$$ $$(2)Q_d=-220-5P$$ $$(3)Q_s=Q_d$$
You can substitute the first and second equations, into the third, like so:
$$-20 + 3P = -220 - 5P$$ All I've done there, is taken the value of Qs from equation 1, and substituted into equation 3. Similarly, I've taken the value of Qd from equation 2, and substituted into equation 3. We can do that, because the supplier and consumer see the same price.
Solving that in the usual way would give you the equilibrium price, for the untaxed scenario. And once you've got that, you can get the equilibrium quantity, too.
Now, what happens with tax t? Is it still the case that supplier and consumer see the same price? If not, can you express the price that one sees, in terms of the price the other sees, and the tax?
Having gone through that, you can then revise either equation 1 or equation 2. You can then substitute equations 1 and 2 into equation 3, and solve as before, to get the new equilibrium price. And once you've got that, you can put that into either equation 1 or 2, to get the new equilibrium quantity. And from there, you can calculate the tax yield.