--%>
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 : Public utilities in natural monopoly

    Public utilities are generally: (1) regulated natural monopolies. (2) competitive non-profit corporations. (3) consequences of diseconomies of scale in production. (4) only subject to laissez-faire regulation. (5) operated by the federal government.

    		•
  • Q : Reducing prices due to a commodity

    Which of the given would NOT be taken as predatory behaviour: (w) Rapid technological innovation. (x) Reducing prices due to a commodity surplus. (y) Duplicative products intended to absorb shelf space. (z) Introduction of close substitutes for rivals

    		•
  • Q : Exploiting the economies of Scope Bobby

    Bobby Lee’s dairy has gainfully expanded beyond butter, fresh milk and cheese, by providing Organizmic Fertilizer, guided by ATV tours for the visitors, and Granny Lee’s Exfoliating Body Yogurt. The Clyde County Business News trumpets that the Bobby Lee ha

    		•
  • Q : Sunk cost Give the answer of following

    Give the answer of following question. Which of the following sayings associate most closely to the idea of sunk costs? 1) Don't cry over spilt milk. 2) A bird in the hand is worth two in the bush. 3) He who hesitates is lost. 4) Show me the money.

    		•
  • Q : Bank rate on money supply What will be

    What will be the consequence of a rise or fall in the bank rate on money supply? Answer: It will reduce or raise the money supply.

    		•
  • Q : Non-discriminating firm with monopsony

    I have a problem in economics on Resources and Products Flow Model. Please help me in the following question. The non-discriminating firm with the monopsony power in labor market confronts a: (1) Wage rate which consistently surpasses the marginal rev

    		•
  • Q : Features of Indifference Curve Describe

    Describe the features of Indifference Curve? Answer: A) Indifference curves slopes downward from left to right.B) Indifference curves are Convex to origin. C) Two Indifference curve not at all intersect

    		•
  • Q : Negative externalities in production

    Production which generates negative externalities: (w) would lead to underproduction and overpricing of goods. (x) increases producers’ costs of production. (y) increases consumers cost of purchasing the good. (z) would cause the market price of

    		•
  • Q : Equilibrium in the long run This would

    This would be a fallacy to suppose that: (w) a purely competitive firm’s demand curve is perfectly elastic. (x) a purely competitive firm’s supply curve is the marginal cost above the minimum point of the AVC. (y) purely competitive firms generate where MR

    		•
  • Q : Problem on buying a used car You desire

    You desire to purchase a used car. The dealer knows accurately how well the car works and how much it must cost, although you are not sure of its value. This is an illustration of: (i) Asymmetric information. (ii) Dealer rights. (iii) Predatory pricing. (iv) First mov

    		•