Asked by Abder-rahmane Cisse on Jun 13, 2024
Verified
The European demand for access to satellite transmissions can be divided into three groups: A, B, and C. The demand curves for the three groups are:
PA = 500 - 2QA (for Q < 250)
PB = 300 - QB (for Q < 300)
PC = 400 - 2QC (for Q < 200),
where Q = number of hours access per month, and P = price per hour. Satellite transmission is a pure public good with zero marginal cost.
a. Explain the difference between horizontal and vertical summation of demand curves. Derive the horizontally and vertically summed demand curves. Explain the circumstances under which vertical summation is appropriate. When is horizontal summation appropriate?
b. Determine the efficient quantity of satellite service. Explain the process of finding the efficient quantity including a justification for the demand curve. What price is optimal?
Vertical Summation
A method used to derive the market demand curve by adding the quantities demanded by all individuals at each price level, vertically.
Horizontal Summation
A method used to determine the total market demand or supply curve by adding individual demands or supplies at each price level, assuming they are compatible.
Public Good
A commodity or service that is provided without profit to all members of a society, either by the government or a private individual or organization.
- Outline the distinctions between public goods and common property resources, emphasizing their specific attributes and the hurdles faced during provision.
- Apply the tenets of economic theory to evaluate how public goods affect the welfare of society, including an examination of free-rider dilemmas.
Verified Answer
RM
Rakhmatjon MakhamadjonovJun 16, 2024
Final Answer :
a.Horizontal summation implies that the addition is taking place across quantities. Horizontal summation is appropriate when demands are competing. Competing demands imply the consumption by one individual detracts from the potential enjoyment of others.
Vertical assumption is appropriate when demands are non-competing so that consumption by one individual does not detract from the potential for others to enjoy the good. Non-competing demands imply zero marginal cost for additional users. Vertical summation implies that addition is across price.Vertical summation
P = PA + PB + PC
P = [(500 - 2QA) + (300 - QB) + (400 - 2QC)]
P = 1,200 - 5Q
To sum horizontally, we solve for Q (for Q < 200)
PA = 500 - 2QA
QA = 250 - 0.5PA
PB = 300 - QB
QB = 300 - PB
PC = 400 - 2QC
QC = 200 - 0.5PC
Q = QA + QB + QC
Q = [(250 - 0.5PA) + (300 - PB) + (200 - 0.5PC)]
Q = 750 - 2P
b.Since satellite transmission is a public good, the demands are non-competing. This suggests that a vertically summed demand curve is appropriate. Efficiency requires that P be set equal to MC, i.e., 0. This occurs where![a.Horizontal summation implies that the addition is taking place across quantities. Horizontal summation is appropriate when demands are competing. Competing demands imply the consumption by one individual detracts from the potential enjoyment of others. Vertical assumption is appropriate when demands are non-competing so that consumption by one individual does not detract from the potential for others to enjoy the good. Non-competing demands imply zero marginal cost for additional users. Vertical summation implies that addition is across price.Vertical summation P = P<sub>A</sub> + P<sub>B</sub> + P<sub>C </sub> P = [(500 - 2Q<sub>A</sub>) + (300 - Q<sub>B</sub>) + (400 - 2Q<sub>C</sub>)] P = 1,200 - 5Q To sum horizontally, we solve for Q (for Q < 200) P<sub>A</sub> = 500 - 2Q<sub>A </sub> Q<sub>A</sub> = 250 - 0.5P<sub>A </sub> P<sub>B</sub> = 300 - Q<sub>B </sub> Q<sub>B</sub> = 300 - P<sub>B </sub> P<sub>C</sub> = 400 - 2Q<sub>C </sub> Q<sub>C</sub> = 200 - 0.5P<sub>C </sub> Q = Q<sub>A</sub> + Q<sub>B</sub> + Q<sub>C </sub> Q = [(250 - 0.5P<sub>A</sub>) + (300 - P<sub>B</sub>) + (200 - 0.5P<sub>C</sub>)] Q = 750 - 2P b.Since satellite transmission is a public good, the demands are non-competing. This suggests that a vertically summed demand curve is appropriate. Efficiency requires that P be set equal to MC, i.e., 0. This occurs where i.e., where prize for consumer B is equal to 0.](https://d2lvgg3v3hfg70.cloudfront.net/TB3095/11eab6a8_3913_533b_9bd3_815c55cb571b_TB3095_11.jpg)
i.e., where prize for consumer B is equal to 0.
Vertical assumption is appropriate when demands are non-competing so that consumption by one individual does not detract from the potential for others to enjoy the good. Non-competing demands imply zero marginal cost for additional users. Vertical summation implies that addition is across price.Vertical summation
P = PA + PB + PC
P = [(500 - 2QA) + (300 - QB) + (400 - 2QC)]
P = 1,200 - 5Q
To sum horizontally, we solve for Q (for Q < 200)
PA = 500 - 2QA
QA = 250 - 0.5PA
PB = 300 - QB
QB = 300 - PB
PC = 400 - 2QC
QC = 200 - 0.5PC
Q = QA + QB + QC
Q = [(250 - 0.5PA) + (300 - PB) + (200 - 0.5PC)]
Q = 750 - 2P
b.Since satellite transmission is a public good, the demands are non-competing. This suggests that a vertically summed demand curve is appropriate. Efficiency requires that P be set equal to MC, i.e., 0. This occurs where
i.e., where prize for consumer B is equal to 0.
Learning Objectives
- Outline the distinctions between public goods and common property resources, emphasizing their specific attributes and the hurdles faced during provision.
- Apply the tenets of economic theory to evaluate how public goods affect the welfare of society, including an examination of free-rider dilemmas.