# CAE 1 (2017)

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 Universidad Universidad de Barcelona (UB) Grado Administración y Dirección de Empresas - 1º curso Asignatura Microeconomía Año del apunte 2017 Páginas 13 Fecha de subida 19/06/2017 Descargas 1 Puntuación media Subido por jbayona75

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CAE 1 Consider the following supply and demand curves in the market for a good: - Supply: Demand: P= 5 + ½ QS P= 20 - QD Compute the market equilibrium, analyze the welfare effects and show in the graph the different situations that are proposed.
5 + ½ Q = 20 – Q; P (QS) = 5 + ½ · 10; Q + ½ Q = 20 – 5; P = 10 3/2 Q = 15; P (QD) = 20 - 10 Q = 10 P = 10 Graph: 20 Price 15 10 Demand Market equilibrium 5 0 0 5 10 Quantity 15 20 CAE 1 a) At this equilibrium P and Q, what is the consumer surplus value, the producer surplus value and the total surplus value? 20 Price 15 10 Demand Market equilibrium 5 0 0 5 10 15 20 Quantity Consumer surplus= Producer surplus = (20 − 10 ) · ( 10 −0 ) 2 (10 −5 ) · ( 10 −0 ) 2 = = Total surplus = Cs + Ps = 50 + 25; Ts = 75 10 · 10 ; Cs=50 2 5 · 10 2 ; Ps = 25 CAE 1 b) Suppose that a price floor is imposed at P = 15; analyze the welfare effects of this government measure. Can you tell who gains and who loses under a price floor? 20 Price 15 10 Demand Market equilibrium Price ceiling 5 0 0 5 10 15 20 Quantity Consumer surplus = Producer surplus = (20 − 15 ) · ( 5 −0 ) 2 (7,5 −5 ) 2 = 5·5 2 ; Cs = 12,5 + (15 – 7,5) · 5; Ps = 43,75 Total surplus = Cs + Ps = 12,5 + 43,75; Ts = 56,25 The government is the one that gains thanks to this price; price is higher for the consumers and for this reason the demand is smaller, which becomes a bad thing for producers, which almost double their surplus.
There’s market inefficiency as the original total surplus is higher than the total surplus due to the price floor (75 > 56,25).
This welfare decrease is equal to the deadweight loss, which is the gain that the government has due to this price floor.
Deadweight loss = (15 −7,5 ) · ( 10 −5 ) 2 ; DL = 18,75 CAE 1 Suppose that a price ceiling is imposed at P = 15; analyse the welfare effects of this government measure. Can you tell who gains and who loses under a price ceiling? 20 15 Price c) 10 Demand Market equilibrium Price ceiling 5 0 0 5 10 15 20 Quantity As price ceiling is set above the equilibrium price, it is non-binding price floor, which means it has no effect in here, so all the surplus values, the welfare…continue the same as the ones in the first graph.
Cs = 50 Ps = 25 Ts = 75 CAE 1 Government tax = 6€/unit in all producers (supply curve shift by the amount of the tax). Make an equation for the new supply and solve the new equilibrium. New price for consumers? New price received by producers? What quantity and proportion of the 6€/unit tax has been borne by consumers? And by producers? What are the total tax revenues collected by the government? At this new equilibrium what is the consumer, producer and total surplus value? Compute this welfare loss.
Supply: P - 6 = 5 + ½ QS Demand (the same): P = 20 – QD New equilibrium: 5 + ½ Q + 6 = 20 – Q; P – 6 = 5 + ½ Qs; ½ Q + Q = 20 - 6 – 5; P – 6 = 5 + 3; Ps = 14 3/2 Q = 9; Q = 6 P = 20 – Q; Pc = 14 Then, the equilibrium quantity is 6, the price received by consumers is 14 and the one received by producers is 8 (Ps-T = 14 – 6 = 8).
20 18 16 14 12 Price d) 10 Demand Market equilibrium New supply New Market equilibrium 8 6 4 2 0 0 2 4 6 8 10 12 14 16 18 20 Quantity Tax burden faced by consumers = (14 – 10) · (6 – 0); TBc = 24 Tax burden faced by producers = (10 – 8) · (6 – 0); TBc = 12 CAE 1 d) II Tax revenue = (6 – 0) · (14 – 8) = 6 · 6; GTR = 36 Consumer surplus = Producer surplus = (20 − 14 ) · ( 6 − 0 ) 2 ( 8− 5 ) · ( 6 − 0 ) = 2 = 36 ; Cs = 18 2 18 ; Ps = 9 2 Total surplus = Cs + Ps + GTR = 18 + 9 + 36; Ts = 63 Deadweight loss = (14 − 8 ) · (10 − 0 ) = 2 60 ; DL = 30 2 There’s a welfare loss of 12, as the original total surplus was 75.
CAE 1 e) Government tax = 6€/unit in all consumers (supply curve shift by the amount of the tax). Make an equation for the new supply and solve the new equilibrium. New price for consumers? New price received by producers? What quantity and proportion of the 6€/unit tax has been borne by consumers? And by producers? What are the total tax revenues collected by the government? At this new equilibrium what is the consumer, producer and total surplus value? Compute this welfare loss.
Demand: P + 6 = 20 - QD Supply (the same): P = 5 + ½ Qs New equilibrium: 5 + ½ Q = 20 – Q - 6; Pc + 6 =20 – QD; ½ Q + Q = 20 - 6 – 5; P = 20 – QD - 6; Ps = 8 3/2 Q = 9; Q = 6 P = 5 + ½ Qs; Pc = 8 Then, the equilibrium quantity is 6, the price received by producers is 8 and the one received by consumers is 14 (Pc+T = 8 + 6 = 14).
20 18 16 14 Price 12 10 Demand Market equilibrium New market equilibrium 8 6 4 2 0 0 2 4 6 8 10 12 14 16 18 20 Quantity Tax burden faced by consumers = (14 – 10) · (6 – 0); TBc = 24 Tax burden faced by producers = (10 – 8) · (6 – 0); TBc = 12 CAE 1 e) II Tax revenue = (6 – 0) · (14 – 8) = 6 · 6; GTR = 36 Consumer surplus = Producer surplus = (20 − 14 ) · ( 6 − 0 ) 2 ( 8− 5 ) · ( 6 − 0 ) = 2 = 36 ; Cs = 18 2 18 ; Ps = 9 2 Total surplus = Cs + Ps + GTR = 18 + 9 + 36; Ts = 63 Deadweight loss = (14 − 8 ) · (10 − 0 ) = 2 60 ; DL = 30 2 There’s a welfare loss of 12, as the original total surplus was 75.
CAE 1 f) Open economy with free trade: international price for a good is 7€. New equilibrium? Consumer and producer surplus and how much each one gain from foreign trade? How much is the gain or loss to the whole domestic economy? 20 18 16 14 Price 12 10 Demand Market equilibrium International price 8 6 4 2 0 0 2 4 6 8 10 12 14 16 18 20 Quantity P = 5 + ½ Qs; P = 20 – QD; 7 = 5 + ½ Qs; 7 = 20 – QD; 7 – 5 = ½ Qs; QD = 20 - 7; (7 – 5) · 2 = Qs; QD = 13 Qs = 4 Consumer surplus = (20 − 7 ) · ( 13 −0 ) 2 = 13 · 13 ; Cs = 2 84,5 Producer surplus = (7 − 5 ) · ( 4 −0 ) 2 = 2·4 ; Ps = 4 2 Total surplus = Cs + Ps = 84,5 + 4; Ts = 88,5 CAE 1 Thanks to this trade, there’s an amount that consumers gain and also an amount that producers lose.
Consumers gain = 10 · 3 + = 30 + 3·3 2 (13 −10 ) · ( 10 −7 ) 2 = = 30 + 4,5 = 34,5 It also can be found by this other way: Consumers gain = Actual Cs – Original Cs = 84,5 – 50 = 34,5 Producers lose = (4-0) · (10-7) + =4·3+ 6·3 2 (10 − 4 ) · ( 10− 7 ) 2 = = 12 + 9 = 21 It also can be found by this other way: Producers gain = Actual Ps – Original Ps = 4 - 25= - 21 Welfare increase = (13 − 4 ) · ( 10− 7 ) 2 = 9· 3 ; W = 13,5 2 Welfare change = Actual surplus – Original surplus = 88,5 – 75 = 13,5 The change in welfare is a gain of 13,5, which corresponds to the light green area.
This welfare increase or gain is also the gain in the whole domestic economy.
CAE 1 g) Now there’s a 2€ tariff imposed on every imported quantity. New quantity imported after the tariff? Consumer surplus? Domestic consumers better or worse off after tariff? Producer surplus? Domestic producers better or worse off? Value of total taxes generated by government? Domestic economy better or worse off? Deadweight loss value? 20 18 16 14 Price 12 10 Demand Market equilibrium International price New international price 8 6 4 2 0 0 2 4 6 8 10 12 14 16 18 20 Quantity As the tariff is 2€/unit, the new international price is 7 + 2, which is 9.
So now, new demand and supply quantities are: P = 5 + ½ Qs; P = 20 – QD; 9 = 5 + ½ Qs; 9 = 20 – QD; 9 – 5 = ½ Qs; QD = 20 - 9; (9 – 5) · 2 = Qs; QD = 11 Qs = 8 Consumer surplus = (20 − 9 ) · ( 1 1− 0 ) 2 = 1 1· 1 1 ; Cs = 2 60,5 Csloss = Cs after tariff – Cs before tariff = 60,5 – 84,5 = - 24 Consumers has lost surplus, which means this tariff is worse off for them.
CAE 1 Producer surplus = ( 9− 5 ) · ( 8 − 0 ) 2 = 4·8 ; Ps = 16 2 Psgain = Ps after tariff – Ps before tariff = 16 – 4 = 12 Producers has won surplus, which means this tariff is better off for them.
Total surplus = Cs + Ps = 60,5 + 16; Ts = 76,5 Total surplus after tariff decreases in relation with total surplus before tariff, which means there’s welfare loss.
WL = Ts after tariff – Ts before tariff = 76,5 – 88,5; WL = -12 Nevertheless, there’s a welfare gain or increase in total surplus in relation to the original surplus (the total surplus before international trade).
WG = Ts after tariff – Ts original = 76,5 – 75; WG = 1,5 This increase in welfare corresponds to the light green area: Increase in welfare = (10 − 9 ) · ( 11 − 8 ) 2 = 1·3 ; WG = 1,5 2 The domestic economy is worse off because if we compare the increase in welfare after and before tax we can find the loss in domestic economy: DeL = - = IWL after tax – IWL before tax = 13,5 – 1,5; DeL = 12 The government gain thanks to the tariff is the same as the tax revenue, which corresponds with the red area: TR = (11 – 8) · (9 – 7) = 3 · 2; TR = 6 The deadweight loss value is the sum of the two blue triangles: CAE 1 DL = 4·2 2 =2+4 DL = 6 (13 −11 ) · ( 9 −7 ) 2 + ( 8− 4 ) · ( 9 −7 ) 2 = 2·2 2 + ...

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