Let the demand function be [tex]$Qd =3000-50 P$[/tex] and the supply function be [tex]$Qs =-1500+$ 50P$[/tex].
(a) Determine consumer's surplus, producer's surplus, and total surplus.
(b) Suppose the government follows a price floor policy and fixes the price at Rs 51. What will be the effect on consumer's surplus, producer's surplus, and total surplus?
Answer (2)
Find the equilibrium price and quantity by setting Q d = Q s , resulting in P e = 45 and Q e = 750 .
Calculate consumer surplus (CS) and producer surplus (PS) at equilibrium: CS = 5625 and PS = 5625 , with total surplus TS = 11250 .
With a price floor of 51, find the new quantity demanded Q d f = 450 and quantity supplied Q s f = 1050 , with quantity transacted Q = 450 .
Calculate the new consumer surplus C S f = 2025 , producer surplus P S f = 9450 , and total surplus T S f = 11475 , with changes Δ CS = − 3600 , Δ PS = 3825 , and Δ TS = 225 . The final answer is: CS = 5625 , PS = 5625 , TS = 11250 ; Δ CS = − 3600 , Δ PS = 3825 , Δ TS = 225
Explanation
Problem Analysis We are given the demand function Q d = 3000 − 50 P and the supply function Q s = − 1500 + 50 P . We need to find the consumer surplus, producer surplus, and total surplus in equilibrium and with a price floor of Rs 51.
Finding Equilibrium First, we need to find the equilibrium price and quantity by setting the demand equal to the supply: 3000 − 50 P = − 1500 + 50 P
Calculating Equilibrium Price Solving for P , we get: 100 P = 4500 P = 45 So the equilibrium price P e = 45 .
Calculating Equilibrium Quantity Now, we substitute the equilibrium price into either the demand or supply function to find the equilibrium quantity. Using the demand function: Q e = 3000 − 50 ( 45 ) = 3000 − 2250 = 750 So the equilibrium quantity Q e = 750 .
Calculating Consumer Surplus Next, we calculate the consumer surplus (CS). The maximum price is the price when Q d = 0 , so 0 = 3000 − 50 P , which gives P ma x = 60 . Thus, CS = 2 1 × ( P ma x − P e ) × Q e = 2 1 × ( 60 − 45 ) × 750 = 2 1 × 15 × 750 = 5625
Calculating Producer Surplus Now, we calculate the producer surplus (PS). The minimum price is the price when Q s = 0 , so 0 = − 1500 + 50 P , which gives P min = 30 . Thus, PS = 2 1 × ( P e − P min ) × Q e = 2 1 × ( 45 − 30 ) × 750 = 2 1 × 15 × 750 = 5625
Calculating Total Surplus The total surplus (TS) is the sum of consumer surplus and producer surplus: TS = CS + PS = 5625 + 5625 = 11250
Quantity Demanded with Price Floor Now, let's analyze the effects of the price floor. With a price floor of P f = 51 , the quantity demanded is: Q d f = 3000 − 50 ( 51 ) = 3000 − 2550 = 450
Quantity Supplied with Price Floor The quantity supplied is: Q s f = − 1500 + 50 ( 51 ) = − 1500 + 2550 = 1050
Quantity Transacted with Price Floor Since it's a price floor, the quantity transacted will be the minimum of Q d f and Q s f . In this case, Q = min ( 450 , 1050 ) = 450 .
New Consumer Surplus The new consumer surplus is: C S f = 2 1 × ( 60 − P f ) × Q d f = 2 1 × ( 60 − 51 ) × 450 = 2 1 × 9 × 450 = 2025
New Producer Surplus The new producer surplus is: P S f = ( P f − 30 ) × Q d f = ( 51 − 30 ) × 450 = 21 × 450 = 9450
New Total Surplus The new total surplus is: T S f = C S f + P S f = 2025 + 9450 = 11475
Change in Consumer Surplus The change in consumer surplus is: Δ CS = C S f − CS = 2025 − 5625 = − 3600
Change in Producer Surplus The change in producer surplus is: Δ PS = P S f − PS = 9450 − 5625 = 3825
Change in Total Surplus The change in total surplus is: Δ TS = T S f − TS = 11475 − 11250 = 225
Final Answer In summary: (a) Consumer Surplus = 5625, Producer Surplus = 5625, Total Surplus = 11250 (b) With a price floor of Rs 51: New Consumer Surplus = 2025, New Producer Surplus = 9450, New Total Surplus = 11475. The change in Consumer Surplus is -3600, the change in Producer Surplus is 3825, and the change in Total Surplus is 225.
Examples
Understanding consumer and producer surplus is crucial in economics for analyzing market efficiency and the impact of government policies. For instance, consider a local farmers market where the demand and supply of organic vegetables determine the prices. If the government sets a price floor to support farmers, it can lead to changes in consumer and producer surplus. By calculating these surpluses, economists can assess whether the policy benefits society as a whole or creates unintended consequences, such as reduced consumer welfare or surplus production.
At equilibrium, the consumer surplus is 5625, producer surplus is 5625, and total surplus is 11250. Implementing a price floor of Rs 51 results in a consumer surplus of 2025, producer surplus of 9450, and a total surplus of 11475. This leads to a decrease in consumer surplus and an increase in producer surplus, with a slight overall increase in total surplus.
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