--%>
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 : Profit for purely competitive firms in

    Profit for purely competitive firms tends in the direction of zero in the long run since: (w) managers resist charging more than a fair price. (x) firms collude to charge prices which barely cover average costs. (y) profit attracts entry, whereas loss

    		•
  • Q : Depending LEAST interest rate Into the

    Into the long run, interest rates depend LEAST upon the: (1) premiums needed to induce savers to delay consumption. (2) premiums necessary to induce wealth holders to sacrifice liquidity. (3) productivity of new capital. (4) demands and supplies of lo

    		•
  • Q : Decrease the burden of sales tax on low

    To decrease the burden of a sales tax upon low income households, in that case: (i) goods along with high income elasticities should be taxed. (ii) goods along with low income elasticities should be taxed. (iii) goods along with high income elasticities must be exempt

    		•
  • Q : What is the revenue of a firm Revenue

    Revenue of a firm: It is the sale or money receipts from the sale of product.

    		•
  • Q : Monopolistic competition in market power

    A firm which has some market power but for that long-run profit is prevented by freedom of entry and exit is engaged within: (1) pure monopoly. (2) pure oligopoly. (3) monopolistic competition. (4) socially responsible behavior. (5) pure competition.<

    		•
  • Q : Wage discrimination Wage discrimination

    Wage discrimination due to race or sex occurs while: (w) members of some groups are paid less for equal work than other groups. (x) certain groups are excluded from particular occupations. (y) housing conditions are inequitable between economic classe

    		•
  • Q : Relative Income to Measures and

    From 1976 year, after adjusting income for taxes and transfers, the relative income group which, according to the Department of the Census, which has decreased most markedly like a percentage of the U.S. population ha

    		•
  • Q : Contradiction of the law of diminishing

    Can someone help me in finding out the right answer from the given options. Which of the following below seems the contradiction of the law of diminishing marginal utility? (1) Ken enjoys his 13th beer of the evening more than his initial. (2) Joan recognizes that her

    		•
  • Q : Income elasticity of positive and

    This given figure as in below demonstrates how consumption of goods A, B, C and D varies like a family’s income changes. Since income rises, the income elasticity of demand is positive and increasing for: (w) good A. (x) good B  (y) good C.

    		•
  • Q : Occurrence of the price discrimination

    Price discrimination occurs when a good is: (1) priced by a formula yielding monopoly profit. (2) denied to customers who refuse to pay the going price. (3) sold at different prices not reflecting differences in costs. (4) subject to government price

    		•