--%>
Assignment Help - homework help

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 : Tax on a good tends to make The tax on

    The tax on a good tends to make: (i) Inflationary pressure the govt. can disperse by cutting its spending. (ii) The wedge among prices buyers pay and the prices sellers obtain. (iii) Rises in supply from the viewpoint of buyers. (iv) More quick transa

    		•
  • Q : Supply law and it's factors State the

    State the Law of supply and explain the factors that affecting supply of commodity

    		•
  • Q : Define normal goods Normal goods:

    Normal goods: Normal goods are such goods whose demand increases with the increase in income of consumer.

    		•
  • Q : What is revenue deficit in government

    Revenue deficit in government budget: Whenever the revenue expenses of the government is more than the revenue receipts it is termed as revenue deficit Revenue expenditure > Revenue receipts

  • Q : Monopsonistic-Wage Discrimination

    Whenever an organization’s wage structure reflects the keenness of individual staff to work, terms which are most applicable comprise: (p) Monopsonistic exploitation & wage discrimination. (q) Monopolistic exploitation and the separation of possession and co

    		•
  • 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 : Competitive Profit Maximization-average

    The purely competitive firm which hires more workers if the value of marginal product of labor increases above the competitively set wage rate will certainly experience rises in its: (1) Overhead costs. (2) Profit per unit. (3) Average variable cost. (4) Marginal reve

    		•
  • Q : Functions of Profits and Losses The

    The functions of profits into a market economy do NOT comprise: (1) stimulation for firms to be innovative and efficient. (2) compensating savers for delays of consumption. (3) signaling changing business conditions. (4) inducing mimi

    		•
  • Q : Dilemma on labor monopsonist The labor

    The labor monopsonist will hire labor up to the point where the marginal: (i) Revenue product of the labor equivalents the wage. (ii) Resource cost of labor equivalents the salary. (iii) Revenue product of labor equivalents its marginal resource cost. (iv) Resource co

    		•
  • Q : Nondiscriminating monopoly Tell answer

    Tell answer of this question.Refer to the following data for a nondiscriminating monopolist. At its profit-maximizing output, this firm will be operating in the: 1) perfectly elastic portion of its demand curve. 2) perfectly inelastic portion of its demand curve. 3)

    		•