--%>
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 : Perfectly inelastic supply of labor

    Glynn’s supply of labor is perfectly inelastic at: (1) point a. (2) point b. (3) point c. (4) point d. (5) point e. 2</span></p> </div> <!-- /comment-box --> </li> </td> </tr><tr> <td> <li> <div class=

    Q : Law of Supply Law of Supply : Supply

    Law of Supply: Supply means the goods provided for sale at a price throughout a particular period of time. This is the capacity and intention of the producers to gen

    		•
  • Q : Exhibiting Predatory Behavior If a firm

    If a firm attempts to drive rivals from its market and after that raises prices and adopts a strategy to deter entry, this is exhibiting: (w) grim strategy. (x) tit-for-tat strategy. (y) predatory behavior. (z) Nash equilibrium.

    Q : Problem on volatility of prices Can

    Can someone help me in finding out the right answer from the given options. In long run, the activities of successful speculators tend to: (i) Decrease the volatility of prices. (ii) Attract legal attention resultant in imprisonment. (iii) Raise the level and volatili

    		•
  • Q : Demand curve for peanuts Question: a)

    Question: a) Johnny consumes peanuts (x1) and a composite good (x2). His utility function is U = x1x2. His marginal utilities are MU1 = x<

    		•
  • Q : Percentage changes in quantity supplied

    The price elasticity of supply can be very approximately computed as the percentage change within: (w) responsiveness of price to variations within the quantity supplied. (x) quantity divided through the intercept coefficient of the supply curve. (y)

    		•
  • Q : Production possibility frontier By

    By using the production possibility frontier, revel that if a society decides to produce more capital goods associated to consumption goods in year 1, then in year 2 there will be more consumption goods.

    		•
  • Q : Problem on Asymmetric Information I

    I have a problem in economics on Problem on Asymmetric Information. Please help me in the following question. Moral hazard and adverse selection are most important in: (1) The United States. (2) Perfectly competitive markets. (3) Internet markets. (4) Markets dominate

    		•
  • Q : What is market Give the answer of

    Give the answer of following question .A market: A) reflects upsloping demand and downsloping supply curves. B) entails the exchange of goods, but not services. C) is an institution that brings together buyers and sellers. D) always requires face-to-face contact betwe

    		•
  • Q : Entry-exit in Long-run equilibrium of

    A competitive industry is in long-run equilibrium only after: (w) net pressure for entry or exit is zero. (x) each firm produces to its capacity. (y) owners reap all the profits they desire. (z) union bosses and firm managers reach mutual agreements.<

    		•