Answer to Question #173201 in Microeconomics for Anuraag

Question

Suppose the market has following demand and supply equations

Demand Qd: 380-10p

Supply Qs: 80 + 5p

p is the price

a) calculate the price at which market is in equilibrium

b) now if the government imposes a fixed tax of r on the suppliers, what will be the price buyers pay and sellers receive, quantity, and government revenue from tax (as function of r). What tax level maximizes the revenue the government collects from tax?

Answer 1

(a) At equilibrium Qd=Qs

$380-10p=80+50p$

$380-80=5p+10p$

$300=15p$

$P=20$

(b)$Q= 380-10p$

$10p=380-Q/10$

$P=38-Q/10$

$Q=80+5p$

$5p=Q-80$

$P=Q/5-16$

Price the suppliers will receive and quantity that will be supplied is calculated below

Supply equition after tax

$P=Q/5-16+r$

$Q/5-16+r=38-Q/10$

$Q/5+Q/10=38+16-r$

$3Q/10=(54-r)$

$Q=180-10r/3$

The quantity supplied will be

$180-10r/3$

The price that suppliers will receive will be

$P=(180-10r/3)/5+16+r$

$P=r/3+52$

Price that consumers will pay is given by

$P=38-Q/10$

$P=38-(180-10r/3)/10$

$P=38-(54-r)/3$

$P=(60+r)/3$

$P=20+r/3$

Government revenue from tax

$=Tax*Quantity$

$r*(180-10r/3)$

$180r+10r$ ²/3

Tax level that maxmizes government revenue

Tax between 0% and 100%