--%>
Assignment Help - homework help

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 : Maximizing profit by hiring labor The

    The firm maximizes profit by hiring the labor at a point where labor’s: (i) Marginal physical product equal its average physical product. (ii) Marginal revenue product equivalents its marginal resource cost. (iii) Rate of exploitation is maximum. (iv) Wage rate

    		•
  • Q : Effect of higher price for normal good

    Let consider the law of demand. The idea that the higher price for a normal good will outcome in less of good being purchased never based logically on the: (1) Income effect, by which the higher price decreases the purchasing power of the income. (2) Demand for good f

    		•
  • Q : When is the DVD sale increased most

    DVD sales are most probably to rise over the long run when the: (w) supply of live entertainment rises. (x) government imposes stiff taxes upon video tapes. (y) technology carries on to advance. (z) prices of theater tickets fall.

  • Q : Freedom of entry in monopolistically

    Along with freedom of entry in a monopolistically competitive market, in long run equilibrium is reached along with firms: (w) earning zero economic profit. (x) producing where price equals marginal cost. (y) producing their most efficient output. (z)

    		•
  • Q : Non-discriminating firm through

    The non-discriminating organization with monopsony power in the labor market confronts the: (i) Wage rate which consistently surpasses the marginal revenue. (ii) MRP less than w. (iii) MFC which surpasses w. (iv) Monopolistic seller of the organization’s output.

    		•
  • Q : Implicit and explicit economic costs I

    I have a problem in economics on Implicit and explicit economic costs. Please help me in the following question. The Economic profit is the difference among total revenue and: (i) The sum of explicit and implicit economic costs. (ii) Accounting cost. (iii) Variable co

    		•
  • Q : Acquire substantial human capital by

    Since philosophers are hardworking and intelligent individuals who should acquire substantial human capital and advanced degrees to work like philosophers, in that case the shaded area B represents: (1) pure profit. (2) consumer surplus. (3) interest

    		•
  • Q : Words of Economic Rent about David

    David Ricardo: (w) was the originator of the theory of pure economic rent onto land. (x) believed that land rent was earned since land would not be available at a zero price. (y) observed that marginal land which is just barely helpful commands positi

    		•
  • Q : Supply of labor at different wage rates

    The time people are willing and capable to work at different wage rates throughout a given period is termed as the: (1) supply of labor. (2) labor force participation rate. (3) marginal product of labor. (4) labor theory of value.

    Q : External costs and external benefits

    Question: (a)         Explain the impact of external costs and external benefits on resource allocation; (b)     

    		•