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THE EFFECT OF SUBSIDIES ON MARKET EQUILIBRIUM
A subsidy is the opposite of a tax, so it is often called a negative tax. Effect of Subsidies : A subsidy given to the production/sale of a good causes the selling price of that good to be lower. As a result, the equilibrium price created in the market is lower than the equilibrium price before or without the subsidy (the equilibrium point shifts lower). With a specific subsidy of s the supply curve shifts parallel downwards, with a lower (smaller) sliver on the price axis. If before the subsidy the supply equation was P = a + bQ, then after the subsidy it will be P' = a + b Q - s = (a - s) + b Q. Since the supply curve is lower, the equilibrium point will be lower. Supply Function before subsidy :P = a + bQ Supply Function after subs :P = a + bQ - s Market equilibrium after subsidy: Qd = Qss or Pd = PssThe subsidy enjoyed by consumers sk = Pe - Pes Subsidy enjoyed by producers sp = s - sk Subsidyprovided by the government : S = s x Qes Sample Problem: The Demand function for a good is shown by the equation P=45-4Q and the Supply function is shown by the equation P=5+Q. The good is subsidized at Rp 4 per unit. a. What is the equilibrium price and equilibrium quantity created in the market before and after the subsidy? b. What is the subsidy enjoyed by consumers, producers and provided by the government? ANSWER: Dik : Pd = 45-4Q Ps= 5+Q A. Qe, Pe, and Qes, Pes? B. sk, sp, and S? A. market equilibrium before subsidies: Pd=PsP=5+Q 45-4Q= 5+Q= 5 + 8 45-5 = Q+ 4QPe = 13 40=5Q Qe = Qe= 8 Market equilibrium after subsidy: s = 4 => Pss = 5 + Q - 4 P s s
= 1 + Q
Pd = (^) Pss P = 45-4Q 45- 4Q
= 1+Q = 45-
44 = 5Q = 45- 35,
Qes =8 .8 (9)Pes = 9.8 (10) B. Subsidy enjoyed by consumers: sk = Pe-Pes = 13- 10 = 3 Subsidy enjoyed by producers: sp = s - sk = 4 - 3 = 1 The subsidy provided by the government: S = s x Qes = 4 x 9 = 36 Example Problem 2: The demand function for a good is given by the equation P= 50-2Q and the supply function is given by the equation P= (-30) +2Q. The good is subsidized at Rp 10 per unit. A. What is the equilibrium price and equilibrium quantity created in the market before and after the subsidy? B. What is the subsidy enjoyed by consumers, producers and provided by the government? ANSWER: Dik : Pd = 50 - 2Q Ps= (-30)+ 2Q A. Qe, Pe, and Qes, Pes? B. sk, sp, and S? A. market equilibrium before subsidies: Pd=PsP = (-30) + 2Q 50-2Q= (-30)+ 2Q= (-30) + 2 (20) 50+30 = 2Q+ 2QPe = (-30) + 40 = 10 80 = 4Q Qe = Qe= 20 Market equilibrium after subsidy: s = 10 => Pss = (-30) + 2Q - 10 P s s
= -40 + 2Q
Pd = (^) Pss P = -40 + 2Q 50- 2Q
= -40+2Q = -40 + 2 (22,5)
90 = 4Q = -40 + 45
Qes = = 22, Pes = 5 B. Subsidies enjoyed by consumers:
Ps = -(a/b) + (1/b)Qs + Tx (Tax implications of raising prices)
Ps = -(a/b) + (1/b)Qs - Sb (Subsidy implication lowers price)
Ps = Supply price Equilibrium price is reached if :
Qd = Qs and Pd = Ps
Supply Function in the presence of Taxes (Tx ) and Subsidies (Sb): Case Example : Given a demand function Qd = 10 - Pd and a supply function Qs = 2 + Ps If tax Tx = 6 or subsidy Sb = 4. Determine the equilibrium price before and after the tax or subsidy! Answer: When equilibrium is reached, Qd = Qs and Pd = Ps 10 - Pd = 2 + Ps or 10 - P = 2 + P -P-P=2 - 10 -2P = - P = -8/- 2 P = 4 Qd = 10 - Pd or Q = 10 - P Q = 10 -(4) Q = Equilibrium before taxes and subsidies is reached at point Eq ( 6 , 4 ) Tax Effect: Pd = 10 - Qd Ps = -2 + Qs + Tx or Ps = -2 + Qs + 6
When equilibrium is reached, Pd = Ps 10 - Qd = -2 + Qs + 6 or 10 - Q = -2 + Q + 6 -Q - Q = -10 -2 + 6 -2Q = -12 + 6 -2Q = - Q = -6/- Q = 3 Q = 10 - P 3 = 10 -P P = 10 - 3 P = 7 Price equilibrium after tax Eq ( 3 , 7) Effect of subsidies: Pd = 10 - Qd Ps = -2 + Qs - Sb or Ps = -2 + Qs - 4 When equilibrium is reached, Pd = Ps 10 - Qd = -2 + Qs - 4 or 10
- Q = -2 + Q - 4 -Q - Q = -10 - 2 - 4 -2Q = - -2Q = - 16 Q = -16/- Q = 8 Q = 10 - P 8 = 10 - P P = 10 - P = 2
P - P1 Q - Q
P2 - P Q2 - Q P - 15.000 Q - 4. = 16.000 - 15.000 3.500 -
P - 15.000 Q - 4.
1.000 - 500 (P - 15,000)(-500) = (Q - 4,000)(1,000) -500P + 7,500,000 = 1,000Q - 4,000,000 1000Q = 4,000,000 + 7,500,000 - 500P Q = 1/ (11,500,000 - 500P) Q = 11,500 - 0.5P ============== So the demand function of the problem above is Q = 11,500 - 0.5P or Q = -1/2P
Third question : In a market known demand function Qd = 40 - 2P and the supply function Ps = Q + 5, based on this information, the equilibrium price occurs at ... Answer: Market equilibrium occurs when Qd = Qs or Pd = Ps, So since we know Qd and Ps, we can substitute the two equations to obtain the equilibrium price. Qd = 40 - 2P and Ps = Q + 5, We substitute it into : Q = 40 - 2(Q + 5) Q = 40 - 2Q - 10 Q = 40-10- 2Q Q = 30 - 2Q Q + 2Q = 30 3Q =
30 Q = 30/3 Q = 10
