Term 1 week 6

Question 1

What is the difference between private and public goods?

Answer 1

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).

Question 2

What are the categories of goods?

Answer 2

Private good - non rival and non excludable
Club good - non rival and excludable
Open access property - fishery, freeway park.
Public good - national defense, lighthouse.

Question 3

How to derive the market demand schedule for private goods?

Answer 3

For private goods
for a particular price you add up quantities.
“Horizontal summation”

Question 4

How do you derive the market demand schedule for public goods?

Answer 4

For public goods
For a particular quantity you add up price.
“vertical summation”.

Question 5

When comparing private and public goods using diagrams with MC what is the difference with efficiency?

Answer 5

At efficient market private provision:
- Private benefits = MC

Whilst at efficient market public provision - the sum of private benefits = MC

Question 6

Why do we have the difference between horziontal and vertical summation when looking at private and public goods?

Answer 6

Because for public goods as it is non-excludeable everyone consumes the same quantity so you look at marginal benefits.

Question 7

What is free riding in public goods?

Answer 7

When one group has to bear all the costs but has to share the benefits.

Question 8

What is the set up for the public good mathematical model?

Answer 8

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

Question 9

In the public good mathematical model what is the difference between the utility function for person A and the budget constraint?

Answer 9

Utility function has all the good G
Whilst budget constraint only has a proportion that person A pays for.

Question 10

What is the samuleson rule?

What does it show?

How else can this samuleson rule be written? And why is this?

Answer 10

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

2. 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.

Question 11

For individual optimum provision of pulbic good how do you find the best response function?
Eg for person A

Answer 11

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

Question 12

How do you draw a best response function for FA and FB

What is particular?

Answer 12

-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

Question 13

What happens when the two reaction functions intercept?

Answer 13

-This gives you the NE contribution.

Question 14

For social optimum provision of public good how do we find it?

Answer 14

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.

Question 15

When finding the optimal social and private provision of public goods what can be concluded?

How can this be explained mathematically?

Answer 15

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.

Question 16

What is the benefit of contributions to free riding?

Answer 16

When one person has to bear the whole cost, it leads to a socially inefficient equilibrium.

Contributions can allow for the provision of a good when no one would supply the good alone.

Question 17

Draw the tragedy of the commons diagramatically

Question 18

Explain the tragedy of the commons?

Answer 18

Assume there is a shared grazing area with cows in two scenarios:

Scenario 1 social planner that wants to maximise village profits

Scenario 2 no one owns the grazing area and want to produce until break even

This causes there to be overgrazing when no one owns the land.

Question 19

How do you set up the tragedy of the commons mathematically?

Answer 19

Assume c cows
production of milk f(c)
Price of milk = p

Social planner maximises profits so
Max (pi) = p . f(c) - pc . c

Whilst individual keeps producing until
f(c) = c .pc