2009

[bear]

 Consider the exchange economy in the above question. Suppose A is endowed
with 3 units of good 1 and 1 unit of good 2, and B is endowed with 1 unit of each
good. A competitive equilibrium is described by the following prices (of goods X and
Y respectively) and allocation of goods.
a) Prices = (1,2) and (xA, yA) = (2.5, 2) , (xB, yB) = (1.5, 0)
b) Prices = (2,1) and (xA, yA) = (2.5, 1.5) , (xB, yB) = (1.5, 0.5)
c) Prices = (1,1) and (xA, yA) = (2, 2) , (xB, yB) = (2, 0)
d) Prices = (1,1) and (xA, yA) = (2.5, 1.5) , (xB, yB) = (1.5, 0.5)


The answer is none of the above. If price vector is (1,1), the equilibrium is (2,2) for A and (2,0) for B. If price vector is (1,2), equilibrium is (2,1) for A and (3,0) for B. Am i on the correct path?

[onionknight]

If the price ratio is 1,1 , there is no equilibrium. None of the options are correct.

[vandita24x7]

Hello onion knight kindly please show the working...

On 8 Jun 2015 12:11, "onionknight [via Discussion forum]" <[hidden email]> wrote:

If the price ratio is 1,1 , there is no equilibrium. None of the options are correct and your claim about the eqm when price ratio is 2,1 is correct

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[bear]

Thanks @onionknight. Why would (1,1) not be a competitive eqm?

PS: Sorry I forgot the utility functions. They are B. A’s utility function is UA =
xA^2+ 4xAyA + 4yA^2 and B’s utility function is UB = xB + yB

[onionknight]

Because at this set of prices, consumer 1 would only like to consume good 2 (since, ua=(xa+2ya)2 ). So he'd like to trade all the 3 units of good 1 for good 2 and given the endowment of 1, this is not feasible.

[vandita24x7]

Please show the working !!!!

On 8 Jun 2015 13:20, "onionknight [via Discussion forum]" <[hidden email]> wrote:

Because at this set of prices, consumer 1 would only like to consume good 2 (since, ua=(xa+2ya)2 ). So he'd like to trade all the 3 units of good 1 for good 2 and given the endowment of 1, this is not feasible.

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[bear]

Thanks @onionknight

[bear]

@Vandita

See, price ratio (ie p1/p2)=1 and MRS=1/2
Whenever MRS<p1/p2, the consumer would prefer good 2.

In competitive eqm, markets should always clear. Given the endowments and preferences, the markets wont clear at price vector (1,1)

Similarly, when price ratio is (1,2) find at what bundles would market clear

[onionknight]

ua= (xa+2xb)2 ub=xb+yb . Indifference curves for both consumers are straight lines (one with slope 2 and one with slope 1). For competitive equilibrium, you only need to find the best bundles for each consumer at different price ratios as you would do in a single consumer case but in addition to both consumers' utility being maximized, you need to ensure market clearing. For instance, at prices 1,2, consumer 1 would be indifferent between the two goods (since the good that costs twice also gives twice the utility per unit), so he would be indifferent between all bundles he could afford. Consumer 2 would prefer to consume good 1 only, and thus he would like to trade one unit of good 2 for two units of good 1 giving a final allocation of (1,2) and (3,0). Thus p1=1 p2=2 (1,2) (3,0) is one possible competitive equilibrium. Hope this helps.

[onionknight]

In your first post, the equilibrium bundle you mentioned at price ratio 1:2 is wrong. It'll be (1,2) (3,0)

[vandita24x7]

Thanks a lot onion knight ! !

On 8 Jun 2015 16:09, "onionknight [via Discussion forum]" <[hidden email]> wrote:

In your first post, the equilibrium bundle you mentioned at price ratio 1:2 is wrong.

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