--%>

Problem on sellers utility function

The economy consists of a single buyer and a single seller. The buyer has the utility function

b ln xB1 + xB2

with b ≤ 10. The seller has the utility function

s ln xS1 + xS2

The buyer is endowed with 0 units of good 1 and 10 units of good 2. The seller is endowed with 1 unit of good 1 and 10 units of good 2.

(i) Find the demand and supply, the inverse demand and the inverse supply functions.
(ii) Find the competitive equilibrium.
(iii) The government imposes a tax on good 1. The tax is t units of good 2 for every 1 unit of good 1 transacted. Find the after-tax competitive equilibrium. What is the effect of this tax on the price paid by the buyer?

E

Expert

Verified

Given: Sellers Utility function and endowment as:

SlnX1S + X2S (1,10)
Buyers as:  blnX1B + X2B (0,10)

Budget constraint for buyer will be: p1x1 + p2x2= p1(0) +p2(10)
Plus at the optimal MRS= Price Ratio

b/x1= p1/p2

Put P2=1 (numeraire)

So  x1B*=B/p1 This is the inverse demand curve

Similarily we do it for seller and we get

s/x1= p1/p2

or  x1*s = s/p1.This is the Inverse  supply curve

b) For competitive equilibrium We know that  total supply In the economy for X1 is 1 that should be equal to demand implies x1*B= B/p1=1 and  p1*= B and P2*= 1

c) There is Only one good 1 in the economy so  there is a tax t for good two and price will be b+t for buyers now and p2=1

   Related Questions in Microeconomics

  • Q : Positive economic profit and accounting

    Purely competitive equilibrium, in long-run firms normally experience positive accounting profit and economic profit which is: (w) also positive, but smaller. (x) zero. (y) negative, but barely that why. (z) either positive, zero, or negative.

  • Q : Theory of mercantilism Explain what was

    Explain what was the theory of mercantilism?

  • Q : Consumers arrival at a point-law of

    According to law of diminishing marginal utility, the consumer inevitably arrives a point where: (i) Net satisfaction derived from good declines. (ii) Consumer suffers from total satiation from some good. (iii) Extra satisfaction outcome by extra unit

  • Q : Labor Unions and Antitrust The legality

    The legality of trade unions as the labor monopolies and illegality of the monopolies in product markets is most rationally described by the: (i) Trade union’s interest in the social welfare and firm’s interest only in gains. (ii) Number of people who adva

  • Q : Multimarket Monopoly A monopolist

    A monopolist operates in two separated markets. The inverse demand functions ofthose markets are given by      and      where   arethe quantities supplied to these markets, respectively. The total cost function facedby the monopolist is &nbs

  • Q : Aggregate effective demand Why,

    Why, according to Keynes, is investment the key economic variable? Why does he think that the volatility of investment spending is likely to cause a problem of aggregate effective demand? Why does he think that this problem can only be solved by government interventio

  • Q : Reduction of consumption of Inferior

    Brian, a poor college student, eats pinto beans or Ramen Noodles for dinner every night. After the graduation, he takes a job with a beginning salary of $50,000 per year. This modification in income is most probable to: (1) Decrease his consumption of both the product

  • Q : Least consistent demand curve with

    The demand curve which is least consistent along with the existence of a substitution consequence is within: (w) Panel A. (x) Panel B. (y) Panel C. (z) Panel D.

    Q : Comparative Advantage in opportunity

    The most important declines in opportunity costs of multiple goods for the consumers and greatest rises in the value of net production for all societies everywhere tend to be realized whenever production is organized in accord by: (1) The optimal clas

  • Q : Hicks Model of Collective Bargaining I

    I have a problem in economics on Hicks Model of Collective Bargaining. Please help me in the following question. The period of union strikes and the equilibrium wage rate at conclusion of a strike are the focus of: (i) Taft-Hartley Act of 1948. (ii) B