Question

Question 5: The demand and supply functions for a good are Pd = 320 – 2Qd and P, = 140 + 3Qs, respectively. If the government provides a subsidy of $40 per unit sold. Outline the distribution of the subsidy, that is, calculate how much of the subsidy is received by the consumer and producer: A: The consumer now pays $232, a decrease of $16 on the equilibrium price with no subsidy ($248) and the producer receives $272, an increase of $24 on the equilibrium price with no subsidy

How is the answer to this A? (with working out please)

Answer 1

Pd =320-2Qd

Ps = 140+3Qs

At Equilibrium, Pd=Ps and Qd=Qs

or, 320-2Q = 140+3Q

or, 3Q+2Q =320-140

or, Q =180/5 = 36

P = 320-2*36 = $248

When Subsidy of $40 is provided to Supplier, then Supply function will be Ps+40 = 140+3Qs

or, Ps = 100+3Qs

Hence At New Equilibrium

or, 320-2Q = 100+3Q

or, 3Q+2Q =320-100

or, Q =220/5 = 44

P = 320-2*44 = $232

Hence Price for Consumer is $232

And Supplier gets $40 on this price, hence Supplier gets 232+40=$272

Hence Consumer gets a subsidy of 248-232 = $16 and Supplier gets a subsidy of 272-248 = $24