The supply equation for a certain product is q−100p+800=0. the demand equation is 400p+q−8000=0. the price p is in dollars.

(a) find the equilibrium point: quantity q=
price p=

(b) suppose a tax of $1 per unit is imposed on the supplier. find the new equilibrium point.
quantity q=
price p=

(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

n=1.75+1.75

step-by-step explanation:

3.5/2=1.75