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The Effect of Taxes and Subsidies on Market Equilibrium, Lecture notes of Economics

Universitas Ibn Khaldun Bogor (UIKB)Economics

The impact of taxes and subsidies on market equilibrium. It discusses how taxes and subsidies affect the price and quantity of a product, and how the tax burden is shared between consumers and producers. The document also provides an example problem to illustrate the concepts. Additionally, it explains how subsidies lead to a lower selling price of a product and how the subsidy amount is shared between consumers and producers. a table and a graph to help visualize the concepts.

Typology: Lecture notes

2017/2018

Available from 02/10/2023

faryz07
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The Effect of Taxes on Market Equilibrium
The Effect of Taxes on Market Equilibrium
If a product is taxed t per unit, there will be a change in the market equilibrium of the product,
both the price and the equilibrium quantity. Usually, the tax burden is partially borne by
consumers, so the price of the product will increase and the quantity demanded will decrease.
Market equilibrium before and after taxation.
The imposition of a tax of t on each unit of the good sold causes the supply curve to shift
upwards, with a larger sliver on the price axis. If before the tax the supply equation was P = a +
bQ, then after the tax it will be P = a + bQ + t
Tax burden borne by consumers : tk = Pe ' - Pe Tax burden
borne by producers : tp = t -
tkTotal tax received by the government : = t x Qe '
Example problem :
Suppose a product is shown with demand function P = 7 + Q and supply function P =
16 - 2Q. The product is taxed at Rp. 3,-/unit
1. What is the market equilibrium price and quantity before and after tax?
2. How much tax revenue does the government receive?
3. How much tax is borne by consumers and producers?
Answer:
1. Pre-tax market equilibrium Qd =Qs
7 + Q= 16 - 2QP = 7 + Q
3Q= 9P = 7 + 3
Qe = 3Pe = 10
So pre-tax market equilibrium E(3,10) Post-tax market
equilibrium
The supply function becomes :
P= 16 - 2Q + t
= 16 - 2Q + 3
= 19 - 2Q Os = Qd
19 - 2Q = 7 + Q
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The Effect of Taxes on Market Equilibrium

The Effect of Taxes on Market Equilibrium If a product is taxed t per unit, there will be a change in the market equilibrium of the product, both the price and the equilibrium quantity. Usually, the tax burden is partially borne by consumers, so the price of the product will increase and the quantity demanded will decrease. Market equilibrium before and after taxation. The imposition of a tax of t on each unit of the good sold causes the supply curve to shift upwards, with a larger sliver on the price axis. If before the tax the supply equation was P = a + bQ, then after the tax it will be P = a + bQ + t Tax burden borne by consumers : tk = Pe ' - Pe Tax burden borne by producers : tp = t - tkTotal tax received by the government : = t x Qe ' Example problem : Suppose a product is shown with demand function P = 7 + Q and supply function P = 16 - 2Q. The product is taxed at Rp. 3,-/unit

  1. What is the market equilibrium price and quantity before and after tax?
  2. How much tax revenue does the government receive?
  3. How much tax is borne by consumers and producers? Answer:
  4. Pre-tax market equilibrium Qd =Qs 7 + Q= 16 - 2QP = 7 + Q 3Q= 9P = 7 + 3 Qe = 3Pe = 10 So pre-tax market equilibrium E(3,10) Post-tax market equilibrium The supply function becomes : P= 16 - 2Q + t = 16 - 2Q + 3 = 19 - 2Q Os = Qd 19 - 2Q = 7 + Q

3Q = 12

Qe ' = 4 P= 19 - 2Q = 19 - 8 Pe ' = 11 So the after-tax market equilibrium E'(4.11)

  1. T= t x Qe ' = 3. 4 = 12 (The amount of tax revenue by the government Rp. 12, -)
  2. tk = Pe ' - Pe = 11 - 10 = 1 (The amount of tax borne by consumers is Rp. 1,-) tp = t - tk = 3 - 1 = 2 (The amount of tax borne by the producer is Rp. 2,-) Effect of Subsidies on Market Equilibrium A subsidy given on the production/sale of a good leads to a lower selling price of that good. If the product is subjected to a subsidy of s per unit, then there will be a decrease in the price of the product and the market equilibrium of the product will also shift. If before tax the supply equation is P = a + bQ, then after tax it becomes P = a + bQ - s Share of subsidy enjoyed by consumers : sk = Pe - Pe' Share of subsidy enjoyed by producers : p = s - skAmount of subsidy paid by government : = s x Qe ' Example Problem : The demand for a commodity is reflected by Qd = 12-2P while the supply Qs = -4 + 2P the government subsidizes Rp. 2 for each unit of the good. a. What is the equilibrium quantity and price before subsidy? b. What is the equilibrium quantity and price after the subsidy? c. What is the share of subsidies for consumers and producers? d. How much subsidy does the government give? Answer;

Pst=a+bQ+t or Pst=Ps+t Formula for Market Balance Before Tax (E) PD=PS or Qd=Qs Formula for Market Balance After Tax (Et) Pd=Pst or Qs=Qst Keteranngan E = initial market equilibrium Et = after-tax market equilibrium S = initial supply function St = After-tax supply function P = demand function Total tax received by the government T = t X Q at Equilibrium after taxation Amount of tax borne by consumer T consumer = (Pet-Pe) X Qt Amount of tax borne by producers T Producer= total tax received by the government - tax borne by consumers Description: Pet :Coordinate P at Market Equilibrium after tax Pe :Coordinate P at market equilibrium before tax Qt :Coordinates of Q at market equilibrium after taxExampleThe demand and supply functions of sugar are given as follows: P 12  Q P Q The government imposes a tax of 4 on each unit produced.Define :

  1. Market equilibrium value before tax.
  2. After-tax market equilibrium value
  3. Draw the curve 4.Total tax received by the government.
  4. The amount of tax borne by consumers
  5. The amount of tax borne by the producer. Answer: From Problem Unknown Pd 12 Q Ps 2 Q t=
  6. The pre-tax Market Equilibrium Value is Pd = Ps 12- Q = 2+Q
  • 2Q = - Q = 5 To determine the value of P, the value of Q is substituted into one of the demand or supply functions.

Q

Q

Pd = 12-Q = 12 - 5 P = 7 Ps = 2+Q = 2+ P = 7 So the market equilibrium value is Q = 5 and P = 7. E(5,7)

  1. Market Equilibrium Value After Tax From the Problem Known : Q  2 t = 4 Market equilibrium formula after tax is Pst=a+bQ+t then Pst=2+Q+ Pst= 6+Q To find the value of P, the value of Q is substituted into the demand function so that the market equilibrium after tax is Et(3,9).
  2. Creating curves a. Creating a Supply chart To graph supply we need some coordinates in order to draw the demand line on the curve. You do this by using a table and the demand function (Pd). Q Q 0 1 2 3 4 5 6 7 8 9 P 12 11 10 9 8 7 6 5 4 3 b. Determine the coordinate points of supply in the same way as a but using the pre-tax supply function (Ps).  2 Q Q 0 1 2 3 4 5 6 7 8 9 P 2 3 4 5 6 7 8 9 10 11 c. The intersection of the demand curve with the supply curve is where the market equilibrium occurs, namely E(5,7). d. Meanwhile, to describe the post-tax market equilibrium curve, we need to find the coordinate points by means of a table and use the taxed supply function (Pst). PD=PSt 12 Q  6 Q  3 So the Q value after tax isQ=3 Q= is substituted inPd Pd=12-Q Pd=12- P= So the value of P after tax is P=9Pst= 6+Q Q 0 1 2 3 4 5 6 7 8 9 P 6 7 8 9 10 11 12 13 14 15 So even from this table, we can see that the market equilibrium after tax is

S = s. Qs Subsidy Amount for Producers SP = S - (Po - Ps) Qs Example Problem; The demand for a commodity is reflected by Q = 12 - 2P while the supply is Q = - 4 + 2P the government provides a subsidy of Rp. 2 per unit of goods. a. What is the equilibrium quantity and price before the subsidy? b. What is the equilibrium quantity and price after the subsidy? c. What share of the subsidy goes to consumers and producers? d. How much is the government subsidizing? Answer; a.) equilibrium quantity and price before subsidy Qd = Qs Q = 12 - 2P 12 - 2P = -4 + 2P = 12 - 8 4P = 16 Q = 4 P = 4 (Market equilibrium before subsidy So (4, 4)) b.) Qd = 12 - 2P =>P = ½ Qd + 6 Pd = Pss Qs = -4 + 2P =>P = - ½ Qs + 2 - ½ Q + 6 = ½ Q Pss = ½ Q + 2 - 2 Q = 6 Pss = ½ Q P = ½ Q P = 3 (Market equilibrium after subsidy Ss ( 6, 3 )c.) size of subsidy to producers SK = (Po - Ps ) Qs SP = S - (( Po - Ps )Qs = ( 4 - 3 ) 6 = 12 - (( 4 - 3 ) 6 ) SK = 6 = 12 - 6 SG = Qs. s Sp = 6 = 6. 2 = 12 (Subsidy amount for producers Rp. 6,-) (Subsidy amount for consumers = Rp. 12,-) d.) Government subsidy S = s. Qs = 2. 6 = 12 The Effect of Taxes on Market Equilibrium A tax imposed on sales always increases the price of the good being offered, so it only affects the supply function, while the demand function remains fixed. After-Tax Bid Function Formula Qs=b(p-t)+a or Qs=a+b(p-t) Pst=a+bQ+t or Pst=Ps+t Formula of Market Balance Before Tax (E) PD=PS or Qd=Qs Formula of Market Balance After Tax (Et)

Pd=Pst or Qs=Qst Keteranngan E = initial market equilibrium Et = after-tax market equilibrium S = initial supply function St = After-tax supply function P = demand function Total tax received by the government T = t X Q at Equilibrium after taxation Amount of tax borne by consumer T consumer = (Pet-Pe) X Qt Amount of tax borne by producers T Producer= total tax received by the government - tax borne by consumers Description: Pet :Coordinate P at Market Equilibrium after tax Pe :Coordinate P at market equilibrium before tax Qt :Coordinates of Q at market equilibrium after taxExampleThe demand and supply functions of sugar are given as follows: P 12  Q P Q The government imposes a tax of 4 on each unit produced.Define :

  1. Market equilibrium value before tax.
  2. After-tax market equilibrium value
  3. Draw the curve 4.Total tax received by the government.
  4. The amount of tax borne by consumers
  5. The amount of tax borne by the producer. Answer: From Problem Unknown Pd 12 Q Ps 2 Q t=
  6. The pre-tax Market Equilibrium Value is Pd = Ps 12- Q = 2+Q
  • 2Q = - Q = 5 To determine the value of P, the value of Q is substituted into one of the demand or supply functions. Pd = 12-Q = 12 - 5 P = 7 Ps = 2+Q

before tax. Here is a picture of the curve.

  1. The total tax received by the government is T = tax x Q at equilibrium after tax T= 4x T= 12
  2. The amount of tax borne by consumers is tk= (Pet-Pe) xQt tk= (9-7)x tk= 6
  3. The amount of tax borne by the producer. tProducer=T Government-T consumer tp = 12- tp= 62. THE EFFECT OF SUBSIDIES ON MARKET EQUILIBRIUM Subsidy (s) is assistance provided by the government to producers of products produced or marketed, so that the prevailing price in the market is lower in accordance with the wishes of the government and the purchasing power of the community increases. The supply function after subsidy is F (Q) = P + S or P = F (Q) - S P P S 0 S 1 Q1 Q2 D Description: Qs :Q value at market equilibrium after subsidy s :Subsidy Po :Value of P in market equilibrium before subsidy Ps: Value of P at market equilibrium after subsidy Sp :Subsidy to Producer SG :Government Subsidy Sk :Consumer Subsidy Market Equilibrium Before subsidy Qd = Qs or Pd=Ps Balance after subsidy Pd = Pss Subsidy to Consumers SK = (Po - Ps) Qs Government subsidy S = s. Qs Subsidy Amount for Producers SP = S - (Po - Ps) Qs Example Problem; Demand for a commodity is reflected by Q = 12 - 2P while

supply Q = -4 + 2P the government provides a subsidy of Rp. 2, - per unit of goods. a. What is the equilibrium quantity and price before the subsidy? b. What is the equilibrium quantity and price after the subsidy? c. What share of the subsidy goes to consumers and producers? d. How much is the government subsidizing? Answer; a.) equilibrium quantity and price before subsidy Qd = Qs Q = 12 - 2P 12 - 2P = -4 + 2P = 12 - 8 4P = 16 Q = 4 P = 4 (Market equilibrium before subsidy So (4, 4)) b.) Qd = 12 - 2P =>P = ½ Qd + 6 Pd = Pss Qs = -4 + 2P =>P = - ½ Qs + 2 - ½ Q + 6 = ½ Q Pss = ½ Q + 2 - 2 Q = 6 Pss = ½ Q P = ½ Q P = 3 (Market equilibrium after subsidy Ss ( 6, 3 )c.) size of subsidy to producers SK = (Po - Ps ) Qs SP = S - (( Po - Ps )Qs = ( 4 - 3 ) 6 = 12 - (( 4 - 3 ) 6 ) SK = 6 = 12 - 6 SG = Qs. s Sp = 6 = 6. 2 = 12 (Subsidy amount for producers Rp. 6,-) (Subsidy amount for consumers = Rp. 12,-) d.) Government subsidy S = s. Qs = 2. 6 = 12 Market Equilibrium Problem Example (1) The demand function for a good is shown by the equation X d = 19 - P, while its supply Xs = -8 + 2P^2. What is the equilibrium price and equilibrium quantity created in the market? Market Equilibrium Problem Example (2) Xd = Xs 19 - P^2 = -8 + 2P^2 27 = 3P^2 9 = P^2 P = 3 Xd = 19 - 32 = 10 So Pe = 3 Xe = 10