Question

Given a demand curve of P = 56 - 1.25Q and a supply curve of P = 6 + 1.25Q, with a subsidy of 30, solve for the dollar value of the added surplus for both consumers (Answer 1) and producers (Answer 2) arising from the subsidy.

Answer 1

P_d= 56- 1.25Q

P_s= 6+1.25Q

Subsidy= 30

With subsidy

P_{d +} Subsidy= P_s

56- 1.25Q + 30= 6+ 1.25Q

56 + 30 - 6 = 1.25Q+ 1.25Q

80= 2.5Q

Q= 32

Total subsidy given by government is

subsidy * Quantity

30*32= $960

Demand price would be = 56- 1.25(32) ( Demand choke price= 56= demand when qty=0)

= 56- 40

= 16

Consumer Surplus= 1/2 (base* height)

=1/2 (32)* (56-16) (base= quantity and height= demand choke price- demand price at 32)

=640

Supply price= 6 + 1.25(32) (Supply choke price= 56= supply when qty=0)

= 6+ 40= 46

Producer surplus= 1/2 (base* height)

= 1/2 (32)* (46-6) (base= quantity and height= supply price at 32 - supply choke price)

= 640

Both consumer surplus and producer surplus after subsidy is $640.