(a) The
equilibrium point is that where the units, q, supplied equals the units, q,
demanded,
Then you can solve the system:
q - 100p + 800 = 0
400p + q - 8000 = 0
The easiest way seems to subtract the first equation from the second one, which
leads to:
400p + 100p - 8000 - 800 = 0 => 500 p - 8800 = 0 =>
=> 500p = 8800
=> p = 8800 / 500 = 17.6
and the quantity is found by solving any of the two initial equations for q:
q - 100p + 800 = 0 => q = 100p - 800 = 100(17.6) - 800 = 1760 - 800 = 960
=> Answer of part (a) q = 960 and p = 17.6
(b) To see the effect of a tax of $1 per unit impossed on the supplier, let's
examine the equations.
While buyers see the same price, p, the demand equation remains the same:
400p + q - 8000 = 0
But the supply changes because the suppliers receive p - 1, so the supply function now is
q - 100(p -1) + 800 = 0
And now solve the new system, by subtracting the supply equation from the deman equation:
400p + q - 8000 - q + 100(p-1) - 800 = 0 =>
400p - 8000 + 100p - 100 - 800 = 0 =>
500 p = 8900 =>
p = 8900 / 500 = 17.8
and q = 8000 - 400p = 8000 - 400(17.8) = 880
Then the new equillibrium is at p = $17.8 and q = 880.
Which means that the price increased the the quantity decreased.
Answer of part (b) = p = 17.8 and q = 880
