Asked by Melissa Jordan on Jun 01, 2024
Verified
In a city with a medium-sized population, the equilibrium price for a city bus ticket is $1.00, and the number of riders each day is 10,800. The short-run price elasticity of demand is -0.60, and the short-run elasticity of supply is 1.0.
a. Estimate the short run linear supply and demand curves for bus tickets.
b. If the demand for bus tickets increased by 10% because of a rise in the world price of oil, what would be the new equilibrium price of bus tickets?
c. If the city council refused to let the bus company raise the price of bus tickets after the demand for tickets increases (see (b) above), what daily shortage of tickets would be created?
d. Would the bus company have an incentive to increase the supply in the long run given the city council's decision in (c) above? Explain your answer.
Price Elasticity of Demand
Measures how much the quantity demanded of a good responds to a change in the price of that good.
Short-Run Elasticity
Measures the responsiveness of demand or supply to price changes over a short period.
Equilibrium Price
The point in the market where the volume of goods available equals the volume of goods sought by buyers.
- Developing linear expressions for supply and demand.
- Analyzing the effects of price controls on the variations in quantity demanded and supplied.
Verified Answer
RK
Rakesh KumarJun 07, 2024
Final Answer :
Given:
P* = $1.00 per ticket Q* = 10,800
Ed = -0.60 Es = 1.0
a.Demand: Qd = a0 + a1P Supply: Qs = b0 + b1P
Use: E = × to compute a1 and b1.
Ed = a1 Es = b1
-0.60 = a1 1.0 = b1
a1 = -6,480 b1 = 10,800
10,800 = a0 - 6,480.00(1.0) 10,800 = b0 + 10,800.00(1.0)
a0 = 17,280 b0 = 0.0
Qd = 17,280 - 6,480P Qs = 0.0 + 10,800P
b.New demand = (1.10)Qd = (17,280 - 6,480P)(1.10)
Qd' = 19,008.00 - 7,128P
Equate Qd' to Qs to get new equilibrium price.19,008 - 7,128P = 0.0 + 10,800 P
P* = $1.06 per ticket
c.The shortage would be the quantity demanded at P = $1.00 minus the quantity supplied at P=$1.00.
Qd = 19,008 - 7,128($1.00) = 11,880
Qs = 0.0 + 10,800($1.00) = 10,800
Shortage = 11,800 - 10,800 = 1,080 rides per day
d.No. The bus company has no incentive to supply more than 10,800 rides per day, as long as the price is restricted at $1.00.
P* = $1.00 per ticket Q* = 10,800
Ed = -0.60 Es = 1.0
a.Demand: Qd = a0 + a1P Supply: Qs = b0 + b1P
Use: E = × to compute a1 and b1.
Ed = a1 Es = b1
-0.60 = a1 1.0 = b1
a1 = -6,480 b1 = 10,800
10,800 = a0 - 6,480.00(1.0) 10,800 = b0 + 10,800.00(1.0)
a0 = 17,280 b0 = 0.0
Qd = 17,280 - 6,480P Qs = 0.0 + 10,800P
b.New demand = (1.10)Qd = (17,280 - 6,480P)(1.10)
Qd' = 19,008.00 - 7,128P
Equate Qd' to Qs to get new equilibrium price.19,008 - 7,128P = 0.0 + 10,800 P
P* = $1.06 per ticket
c.The shortage would be the quantity demanded at P = $1.00 minus the quantity supplied at P=$1.00.
Qd = 19,008 - 7,128($1.00) = 11,880
Qs = 0.0 + 10,800($1.00) = 10,800
Shortage = 11,800 - 10,800 = 1,080 rides per day
d.No. The bus company has no incentive to supply more than 10,800 rides per day, as long as the price is restricted at $1.00.
Learning Objectives
- Developing linear expressions for supply and demand.
- Analyzing the effects of price controls on the variations in quantity demanded and supplied.