Problem on competitive equilibrium of two consumers

The economy consists of two consumers, A and B. Both consumers are endowed with one unit of good 1 and one unit of good 2. Consumer A is entirely indifferent between all consumption plans. Consumer B has the utility function u(xB1 ; xB2 ) = xB1 xB2 .

(i) Find a competitive equilibrium for this economy. (Hint: guess an equilibrium price and then check that it works.)

(ii) Find a second competitive equilibrium (different from the one you found in part (i)).

(iii) Show that the equilibrium is not efficient.

E

Expert

Verified

Budget constraint for person 1:

P1x1 +p2x2 = p1(1) + p2(2)

Similarly  for person 2:

P1x1+ p2x2= p1(1) + p2(2)

Now person 1 will consume according to the MRS= Price Ratio condition and we get:

So we get:
X1* = 1/2 (p1+1)/p1
X2*= 1/2 (p1+1)/p2

Similarily for person 2:
X1*= X1* = 1/2 (p1+1)/p1
X2*= 1/2 (p1+1)/p2

Now total x1* in economy is 2

So p1+1/p1= 2
P1+1= 2P1
So, p1*=1
And p2=1 (numeraire)

So competitive equilibrium:
(1,1) – Person 1
(1,1)- Person 2

b) second competitive equilibrium

(1/3, 2/3) and( 2/3, 1/3)

c) For efficiency MRS1= MRS2

Now x2/x1= x2/x1
For above(Put the values 1/3, 2/3 and 2/3,1/3 in MRS condition 2 not equal to 1

So this is not efficient

   Related Questions in Microeconomics

  • Q : Economic cost Economic cost can best be

    Economic cost can best be defined as: A) any contractual obligation that results in a flow of money expenditures from an enterprise to resource suppliers. B) any contractual obligation to labor or material suppliers. C) compensations that must be received by resource

  • Q : Competitive Profit Maximization Can

    Can someone please help me in finding out the accurate answer from the following question. The profit-maximizing competitive firm hiring from the competitive labor market will be in balance or equilibrium where: (i) w = MRC. (ii) MPP = MRC. (iii) VMP = MPP. (iv) VMP =

  • Q : Determine points where is most price

    Of all of the known ranges on given supply curves, the supply of tanks of dehydrated water is most price elasticity among: (i) point a and point b. (ii) point b and point c. (iii) point c and point d. (iv) point d and point e. (v) point e and point f.

    Q : Sign of Lorenz Curves The Lorenz curve

    The Lorenz curve gives an indication of: (w) the poverty rate. (x) dead end poverty. (y) relative poverty. (z) post-transfer poverty.

    Can someone explain/help me with best solution about problem of Economic

  • Q : Needs a goal of maximizing by

    The long run survival of a purely-competitive firm needs a goal of maximizing: (i) managerial salaries. (ii) total costs. (iii) economic profits. (iv) total revenue. (v) fixed costs to minimize variable costs.

    How

  • Q : Tariffs Choose the right answer from

    Choose the right answer from following. Tariffs: A) may be imposed either to raise revenue (revenue tariffs) or to shield domestic producers from foreign competition (protective tariffs). B) are also called import quotas. C) are excise taxes on goods exported abroad.

  • Q : Short-run supply curve and marginal

    Short-run supply curve of a purely competitive firm’s is the positively sloped part of the marginal cost curve which is above its: (w) average fixed cost curve. (x) resource demand curve. (y) average variable cost. (z) short-run

  • Q : Problem on rational ignorance An

    An illustration of rational ignorance is demonstrated when you: (1) Are elected to a political office. (2) Settle for an other half who is not your "ideal" mate. (3) Eat a steak which increases your cholesterol level. (4) Were suspended from high scho

  • Q : Deterrent Give me answer of this

    Give me answer of this question. Which one of the following is presently a major deterrent to bank panics in the United States? A) the legal reserve requirement B) the fractional reserve system C) the gold standard D) deposit insurance

  • Q : Price mechanism Write down the benefits

    Write down the benefits of leaving the allocation of countries resources to price mechanism?

2015 ©TutorsGlobe All rights reserved. TutorsGlobe Rated 4.8/5 based on 34139 reviews.