Term 1 week 6 Flashcards
What is the difference between private and public goods?
Public goods differ as they are
non-excludable : it is impossible to stop individuals using the good (public park)
non-rival: Someone using it does not mean there is less for another person (street lights).
What are the categories of goods?
Private good - non rival and non excludable
Club good - non rival and excludable
Open access property - fishery, freeway park.
Public good - national defense, lighthouse.
How to derive the market demand schedule for private goods?
For private goods
for a particular price you add up quantities.
“Horizontal summation”
How do you derive the market demand schedule for public goods?
For public goods
For a particular quantity you add up price.
“vertical summation”.
When comparing private and public goods using diagrams with MC what is the difference with efficiency?
At efficient market private provision:
- Private benefits = MC
Whilst at efficient market public provision - the sum of private benefits = MC
Why do we have the difference between horziontal and vertical summation when looking at private and public goods?
Because for public goods as it is non-excludeable everyone consumes the same quantity so you look at marginal benefits.
What is free riding in public goods?
When one group has to bear all the costs but has to share the benefits.
What is the set up for the public good mathematical model?
Two people: person A and person B
Two goods (X private), (G is public good).
The utility function of person A Ua(X^A, G)
The utility function of person B
Ub(X^B,G)
The budget constraint
w^A = pxXA + PgGA
Then make it a total economy
Maximise total
MAX (UA+UB) ST WA+WB = PXXA+PXXB + PGGA+PGGB
FOC W.R.T
XA
XB
G
Then sub XA and XB
Then this = lamda
sub in G for lamda
divide through by delluA/dellg//delluA/dellxA
MRSA G,X + MRSB G,X = 1
In the public good mathematical model what is the difference between the utility function for person A and the budget constraint?
Utility function has all the good G
Whilst budget constraint only has a proportion that person A pays for.
What is the samuleson rule?
What does it show?
How else can this samuleson rule be written? And why is this?
MRS A G,X + MRS B G,X =1
In the case of consumption the MRS must reflect the amount of the private good that all consumers would be willing to give up for an extra unit of the public good
If you give up one unit of the private good how many units of the public good can i get.
MRS is the price you are paying
- MC /MRT
Because MRT of public good and private good is at rate of 1-1
Amount of private good given up to get extra unit of public good.
For individual optimum provision of pulbic good how do you find the best response function?
Eg for person A
You get the full utility function eg
2logXA + log(FA+FB)
S.T 100 = XA +FA
Make everything in terms of F
Then solve for FA to find BRF
How do you draw a best response function for FA and FB
What is particular?
-FA on X axis
-FB on Y axis
Then plot the axis for when they are = 0
When Person B has reached max contribution then person A will not add anymore
What happens when the two reaction functions intercept?
-This gives you the NE contribution.
For social optimum provision of public good how do we find it?
MRS XA,F + MRSXB,F = MRS
Then sub in the marginal utilities of this
To get a new expression
Then sub in economy resource constraint.
When finding the optimal social and private provision of public goods what can be concluded?
How can this be explained mathematically?
The social optimum provision will be higher than private optimum
as when they provide privately they do not account for the externality they can create and therefore free ride.
-Privately, they provide the public good where
MRSA = MRT
MRSB = MRT
But as MRT does not change socially
MRSA +MRSB > MRT
so more of the public good should be provided.
