Assume the market demand and supply for one commodity are y

Assume the market demand and supply for one commodity are y = 1000-5p y = 4p-80 respectively, among which p refers to the price, and prefers to output level. lf the government imposes tax on such a commodity, $9 per unit. Solve for: The equilibrium price paid by the consumers and the price received by the sellers. The deadweight loss caused by such a tax schedule.

Solution

(a)

In equilibrium, demand = supply

1000 - 5p = 4p - 80

9p = 1080

p = 120

y = 4p - 80 = 480 - 80 = 400

(b)

When tax of $9 is imposed, suppliers\' price decreases by $9, so that p = p - 9

Supply schedule becomes: y = 4(p - 9) - 80 = 4p - 116

Equating with demand:

1000 - 5p = 4p - 116

1116 = 9p

p = 124

y = 4p - 44 = 496 - 44 = 452

Deadweight loss caused by tax = (1/2) x Change in price x Change in output

= (1/2) x (124 - 120) x (454 - 420)

= (1/2) x 4 x 34

= 68