Qd=100-20P and Qs=10P+50. Use this to answer the following:

Question

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?

Answer 1

Qd = 100-20p

Qs = 10p + 50

in equilibrium, Qd =Qs = 100-20p = 10p+50

30p=50

p =5/3= $1.67

equilibrium Q = 100- 20(5/3) = (300-100)/3 =200/3 = 66 2/3

tax = $1, shift the supply curve up by one unit

it helps to graph this problem

tax will increase equilibrim price and reduce equiliibrium quantity

supply curve is: 10p+50 = Qs

10p =Qs-50

p = Q/10 -5

add the $1 tax

new after tax supply curve shifts up

p=Q/10-5+1 = Q/10-4

p =Q/10-4 = 50-Q/2

multiply by 10

q-40 = 500-5q

6q =540

q = 540/6 = 60

p = 60/10-4= $2

consumers buy less at a higher price

but that's a $1 per unit tax, not a $1 lump sum tax

a lump sum tax leaves the equilibrium price and quantity the same, and just takes the tax out of profits, like an increase in fixed costs. if after tax profits are positive, the equilibrium is the same. if after lump sum profits are negative, the company just shuts down, sells, or goes into bankruptcy

the consumer gets the same consumer surplus with the government taking the tax from producer surplus or profits