Lecture 2- Walrasian Equilibrium In Pure Exchange Economies

Question 1

What does the Walrasian equilibrium framework aim to do?

Answer 1

Aims to build a framework to analyse how scarce resources should be allocated between different agents in the economy.

Question 2

Aims to build a framework to analyse how scarce resources should be allocated between different agents in the economy.

Answer 2

1. The initial allocation of each agent- We assume we know the initial endowment of each agent.
2. The preferences of each agent- We assume preferences of agents in the economy are given which means each agent will have some sort of utility function

Question 3

What are assumptions 1-3 of the Walrasian Model?

Answer 3

1. There is only exchange in the economy; no production, we assume products were already there and are just exchanged with one another
2. There is well defined property rights. This means every unit of every commodity in the economy has a clear and well defined owner.
3. There is a market for every commodity. There is a price consumers can buy and sell units of every commodity.

Question 4

What are assumptions 4-6 of the Walrasian Model?

Answer 4

4. Everyone is a price taker. In other words the price of which people can buy or sell commodities is the same no matter how much quantity they buy ( no bargaining power)
5. Goods are rivalrous. This means each unit of every good can be consumed by only one individual. One individual consuming a good will mean the other individual cannot consume the good.
6. An agents Utility depends only on the good he consumes and nothing else and nothing else like the price they pay for it.

Question 5

What are assumptions 7-9 of the Walrasian Model?

Answer 5

7. There are no transaction costs to trade, such as transportation or advertisement costs
8. Every individual has rational, complete and transitive preferences and chooses his optimal bundle subject to budget constraint.
9. Markets clear, this means prices are set in a way which ensures demand always equals supply

Question 6

What is step one of computing the walrassian equilibrium and how is this done

Answer 6

Find optimal demand as a function of price . This is done by finding the UMPa and UMPb. For each each set up the utility prefrences subject to the budget constraint which will be P1Xa1+P2Xa2

Question 7

What is step two of solving the walrassian equilibrium and how is this done?

Answer 7

Write out the excess demand vector For Z1(p) and Z2(P). Excess demand is how much is demanded- how much is supplied. For Z1(p) take Xa1 + Xb1-( First number of Ea + first number of Eb) and the same for Z2(p)

Question 8

What is step 3 of computing the Walrassian equilibrium and how to do we do this?

Answer 8

Step 3 is we assume markets clear. We do this by finding prices of p1 and p2 such that Z1(P) and Z2(p)=0. In order to do this we normalise one price in this case lets take p2=1 and then solve for p1. We then plug in values and find Xa(p) and Xb(p) and this provides of with the WE allocation. We are able check if markets clear if Xa1+Xb1=e1

Question 9

What is the Walrarasian law and how can it be used?

Answer 9

The Walrasian law states that P1Z1(p)+P2Z2(p)=0 therefore we can plug in z1(p) and z2(p) and check if our working equals zero if it does then our working is correct.

Question 10

Compute the Walrasian equilbrium and draw the edgeowrth box for A: Ua=2Xa1,Xa2 EA(2,1) B:Ub (2lnXb1+lnXb2) Eb(0,2)

Answer 10

see notes

Question 11

Compute and Edgeworth box for excess demand and excess supply and explain what conditions mean there is no Walrasian equilibrium

Answer 11

See notes