Question

I GOT PARTS 1 AND 2.....ITS 3-8 WHERE IM STUCK AND CONFUSED. PLEASE HELP!
In this activity consider the following demand and supply functions. emand upply D(p) 43660- 230p S(p)- 400p- 8000 ulmé that no taxes are imp 1. First, ass hen find the equilibrium price and quantity 100-230 р: 2. Assume that there is a 10% tax imposed on the consumer, find the new equilibrium price and quantit e 300 3360pa Ruu 3 (p the portion of the tax paid by the producer and the portion of the tax paid by the consumer, and Producer Consumer the tax revenue generated for the government Total Tax

Answer 1

Solution:

We are given demand function as: D(p) = 43660 - 230p

And the supply function as: S(p) = 400p - 8000

1) Equilibrium occurs where demand equals supply. With no taxation, this means D(p*) = S(p*)

43660 - 230p* = 400p* - 8000

43660 + 8000 = (400+230)p*

So, p* = 51660/630 = 82

So, the equilibrium quantity, q*, becomes= 400*82 - 8000 = 24,800

2) With 10% tax imposed on the consumers, prices paid by the consumers increase by (10%), so we will have a modified demand function. Let's denote prices paid by consumers by pc and price received by sellers by ps

Then, demand function: D(pc) = D(p(1+10%)) = 43660 - 230(1.1)p

D(pc) = 43660 - 253p

Since, the tax is not on suppliers, their supply function remains same. So, S(ps) = S(p) = 400p - 8000

a) Finding this new intersection: 43660 - 253p = 400p -8000

p = 51660/653 = 79.11.

New quantity, q= 400(79.11) - 8000 = 23,644

b) Note that p = ps, that is, the price obtained above is price received by sellers (after the tax cut). So price paid by consumers is higher. pc = (1.1)79.11 = 87.02.

So, tax burden born by consumers = (pc - p*)*q = (87.02 -82)*23644 = 118,692.88

And the portion of tax paid by sellers = (p* - ps)*q = (82 - 79.11)*23644 = 68,331.16

c) Finally, tax revenue generated for the government = 118692.88 + 68331.16 = 187,024.04

(This can also be calculated as (pc - ps)*q = (87.02-79.11)*23644 = 187,024.04)

3) Now, if 10% tax is imposed on producers, again like the above part, denoting price paid by consumers by pc and price received by sellers by ps. Now since tax is imposed on sellers, the supply function will be modified and not the demand function.

a) New supply function: S(ps) = S((1-10%)p)

S(ps) = 400(0.9p) - 8000 = 360p - 8000

Demand function remains the same as D(pc) = D(p) = 43660 - 230p

Finding new intersection: D(pc) = S(ps)

43660 - 230p = 360p - 8000

p = 51660/590 = 87.56

New q = 43660 - 230(87.56) = 23,521.2

b) pc = p = 87.56

ps = 0.9*p = 0.9*87.56 = 78.8

So, tax borne by consumers = (pc - p*)*q = (87.56 - 82)*23521.2 = 130,777.872

And tax burden borne by sellers = (p* - ps)*q = (82-78.8)*23521.2 = 75,267.84

c) Tax revenue generated by the govt = 130777.872 + 75267.84 = 206,045.712

4) When $15 tax is imposed on the consumer, this is the wedge between price paid by the consumers and price received by sellers. Thus, pc - ps = 15

a) D(pc) = D(p + 15) = 43660 - 230(p + 15) = 40210- 230p

S(ps) = S(p) = 400p - 8000

So, finding the intersection: 40210- 230p = 400p - 8000

p = 48210/630 = 76.52

So, q = 400*76.52 - 8000 = 22,608

b) Note that p = ps = $76.52; pc = ps + 15 = 76.52+15 = 91.52

So, tax burden born by consumers = (pc - p*)*q = (91.52 -82)*22608 = 215,228.16

And the portion of tax paid by sellers = (p* - ps)*q = (82 - 76.52)*22608 = 123,891.84

c) Finally, tax revenue generated for the government = 215228.16 + 123891.84 = 339,120

5) When $15 tax is imposed on producers, this is again the wedge between price paid by the consumers and price received by sellers. Thus, pc - ps = 15

a) D(pc) = D(p) = 43660 - 230p

S(ps) = S(p - 15) = 400(p - 15) - 8000 = 400p - 14000

So, finding the intersection: 43660- 230p = 400p - 14000

p = 57660/630 = 91.52

So, q = 43660 - 230*91.52 = 22610.4

b) Note that p = pc = $91.52; ps = pc - 15 = 91.52 -15 = 76.52

So, tax burden born by consumers = (pc - p*)*q = (91.52 -82)*22610.4 = 215,251.008

And the portion of tax paid by sellers = (p* - ps)*q = (82 - 76.52)*22610.4 = 123,904.992

c) Finally, tax revenue generated for the government = 215251.008 + 123904.992 = 339,156

6) Note that the government earns maximum tax revenue in the last case. Thus, for the government, the best tax policy is to impose $15 tax on the producer.

7) In same way, we can see that the producers incur minimum tax burden in the first case. So, the best tax policy for the producers is to impose 10% tax on the consumers.

8) Finally, the consumers incur minimum tax share burden when 10% tax is imposed on consumers, so this is the best tax policy for consumers as well.