Question

Assume a perfectly competitive market without externalities. Market Demand is given by P = 25 − 1 4 Q and Market Supply is given by P = 1 3 Q + 8. The government imposes a per-unit tax of t=1.05. What is the change in Producer Surplus because the tax is imposed? Enter a number only, no $ sign. Enter a negative sign if Producer Surplus decreases.

Answer 1

Competitive market determines the Equilibrium Point where Demand curve Intersect Supply curve.

25-14Q=13Q+8

Q=0•63

Substituting value of Q in both equations-----

P= 25-14(0•63)= $16•18

P= 13(0•63)+8=$16•18

See graph ( sketched by putting random values of p in both equations-----

Area ABE depicts Consumers surplus(CS)

Area BLE depicts producers surplus (PS)

# when govt imposes per unit tax of $ 1•05---------:

The supply curve shifts leftward and new equlibrium Point (E') is determined by new supply equation-----

P-1•05= 13Q+8

Or p=13Q+9•05

At Equilibrium-------

25-14Q= 13Q+9•05

Q=15•95/27= 0•59

P= 13(•59)+9•05=$16•72

See graph after per unit tax--------

Area ABE' depicts Consumers surplus

Area BDE' depicts producers surplus.

Table showing change in CS & PS------

Surplus	Before tax($)	After tax($)	change($)
PS	5•28	4•80	-0•48
CS	2•77	2•44	-0•33

This way, we find that due to Imposition of per unit tax by govt, both Consumers surplus as well as producers surplus decreases.

Thanks