Find equilibrium price and quantity? How to find new quantity, price and Incidence of taxation on consumers if a 1 dollar lump sum tax is levied on suppliers?

Question

Quantity demanded=-20P+100

Quantity Supplied=50+10P

I calculated price to be 5/3 and Q as 66.67, but can’t figure out the final part.

Answer 1

Qs = 50 + 10P

a tax of 1 on supliers means P+1

Qs = 50+10P

10P = Qs -50

P = (Qs-50)/10

new P = (Qs-50)/10 + 1

= (Qs -40)/10

Qs -40 = 10P

Qs = 10P +40 = Qd = -20P +100

10P+20P=100-40

30P=60

new P = 2

Qs = 10P+40 = 60

Qd= -20P +100= 60

new equilibrium is P=2, Q=60 with tax =1

it might help to graph the lines with the supply curve shifted up 1

consumers buy less at the higher after tax price

you could also calculate the consumer surplus loss

new CS=.5(5-2)(60) =90, old =.5(5-5/3)(200/3)=1000/9=111 1/9 = triangular areas above the price line, below the demand curve

a loss of 111 1/9 - 90 = 21 1/9