--%>
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 : Profit-maximizing level of output When

    When LoCalLoCarbo, the favorite corporation of fad dieters, produces adequate output to minimize its average total costs that will: (1) produce more than the profit-maximizing level of output. (2) concurrently minimize its average variable cost. (3) p

    		•
  • Q : Long-run In the long-run, an increase

    In the long-run, an increase in consumer desire for strawberries is most likely to:

    		•
  • Q : Defined Welfare Recipients By

    By description, a family of four receives welfare when it: (1) pays a smaller share of taxes than its share of benefits from government. (2) lives below the poverty line. (3) includes a student attending college on an academic scholar

    		•
  • Q : Stable Competitive Economy Into a

    Into a stable competitive economy without innovation, transaction, or uncertainty costs, all accounting profits would be: (w) pure economic profits. (x) payments required to secure owner-provided resources. (y) pure e

    		•
  • Q : How Accounting profits differ from

    Can someone please help me in finding out the accurate answer from the following question. The Accounting profits differ from economic profits in such a manner that: (1) Accounting profits take into account of opportunity costs, whereas economic profits take into acco

    		•
  • Q : Economic efficiency of purely

    Most economists favor purely competitive markets since they tend to as: (1) economies of scale. (2) large profits. (3) mutual interdependence. (4) corporate organizations. (5) economic efficiency. Hello guys I want

    		•
  • Q : Value of the Average Product Hulk is

    Hulk is the fitness counselor who coaches 5 clients at a time in the exercise groups at Beefcake Body Builders. His hourly salary is $17, and Beefcake charges Hulk’s clients $20 for each and every hour-long conditioning session. Average value of the product Hulk

    		•
  • Q : Price times quantity in total revenue

    Total revenue equals: (w) price times quantity. (x) marginal revenue times marginal cost. (y) profit per unit of output. (z) total cost minus profit. Please choose the right answer from above...I want your suggesti

    		•
  • Q : Example of predatory behavior Assume

    Assume that a new Wal-Mart is built just outside a small town, and also Wal-Mart aggressively cuts prices therefore much that the rivals close their doors. In that case, once its rivals exit the market, the Wal-Mart raises prices significantly. Wal-Ma

    		•
  • Q : Illustrates the initial point of

    RoboMatic’s RoboMaids have turn into the hottest innovation in consumer electronics since colour television. The initial point Robomatic requires to see in its quest to maximize profit is: (1) point e. (2) point f. (3) point g.

    		•