--%>
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 : Problem regarding to Government

    Suppose the market for exercise equipment is primarily in equilibrium, and after that the government places a subsidy upon the exercise equipment. The probable result would be: (1) increased production and purchases of exercise equipment. (2) that buy

    		•
  • 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 : Market Supplies of Labor I have a

    I have a problem in economics on Market Supplies of Labor. Please help me in the following question. In long run, the labor supply curve facing the major industry: (i) Will always be positively associated to the wage rate. (ii) Will slope upward if and only if individ

    		•
  • Q : Price increment for higher total revenue

    A price increase for Pixie’s cheesy fried grits by P1 to P2 would yield higher total as: (w) revenue because demand is price elastic. (x) supply since demand is unitarily elastic. (y) revenue since demand is price inelastic. (z) use of the

    		•
  • Q : Monopsonistic Exploitation-MRP and w

    Can someone please help me in finding out the accurate answer from the following question. In the equilibrium for an organization with power to adjust the wage it pays, the rate of monopsonistic exploitation equivalents any differe

    		•
  • Q : Problem on positive quantity Supply The

    The law of supply defines that, other things equivalent: (1) Quantity supplied differs inversely with price. (2) A good’s supply is positively associated to its demand. (3) Quantity supplied is positively associated to price. (4) Prices and cost

    		•
  • Q : Short-run losses of shuts down firm

    When a firm shuts down, short-run losses of it equals total: (w) implicit costs. (x) variable costs. (y) fixed costs. (z) resource costs. I need a good answer on the topic of Economics problems. Pl

    		•
  • Q : Monopolistic competitive firm in normal

    This monopolistically competitive firm in illustrated figure produces Q units as well as experiences: (1) economic profits equal to 0cbQ. (2) economic losses equal to cpab. (3) more than normal accounting profits. (4) marginal cost in excess of averag

    		•
  • Q : Problem of Nash Equilibrium Carlos and

    Carlos and Ivana are room-mates and friends. Carlos and Ivana eat together despite who cooks on a given night. Within this payoff matrix, Nash equilibrium could never be obtained in that: (w) neither Carlos nor Ivana cook, nor do they eat. (x) Carlos

    		•
  • 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)

    		•