--%>
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 : Market structure of monopoly A monopoly

    A monopoly is a type of market structure in that one: (w) seller produces whole industry’s output. (x) giant firm is a price taker. (y) barrier to entry exists. (z) giant firm is the single buyer of resources.

    Q : Surviving for maximum profits in

    Supposing that the competitive firms should seek the maximum profits to survive signifies that: (1) Firm do not make trial-and-error decisions. (2) Each and every firm always seeks the maximum gain and nothing else. (3) Competition is very profitable.

    		•
  • Q : Purely competitive firms in increasing

    When purely competitive firms operate within increasing cost industries, several: (1) individual firms’ supply curves should be horizontal. (2) firms should experience decreasing returns to scale at low output levels. (3) specia

    		•
  • Q : Monopolistic competition and product

    The demand curve facing a monopolistically competitive firm might shift rightward when this: (w) increases wages to workers. (x) experiences a decline in costs. (y) advertises successfully. (z) responds strategically to competitors&rs

    		•
  • Q : Estimation of price elasticity of

    You can calculate approximately a price elasticity of supply by data indicating that: (a) steel production rises 18 % while national income grows 13 %. (b) farmers increase soybean plantings 15 % while prices rise 5 %. (c) Ford raises production when

    		•
  • Q : Horizontal demand curve facing purely

    The demand curve facing a purely competitive firm is: (w) horizontal. (x) vertical. (y) downward sloping. (z) the horizontal summation of individual demand curves. Can someone explain/help me with best solution abo

    		•
  • Q : Determine demand curve for

    A tax will be forward-shifted totally when the demand curve is: (w) downward sloping and the supply curve are horizontal. (x) horizontal and the supply curve is upward sloping. (y) perfectly price inelastic and identical to the supply

    		•
  • Q : Involvement of price makers firms

    Price-maker firms would most likely comprise: (1) a tomato farmer in California. (2) a sheep herder who produces wool in a remote part of New Zealand. (3) a stock broker who contacts customers through the internet. (4) a rural grocery store. (5) the b

    		•
  • Q : Key questions in evaluating a research

    Key questions in evaluating a research report: In brief, there are five key questions you, as a consumer of analytical work, should ask yourself as you are evaluating a research report. 1. What is the purpose of th

    		•
  • Q : Define Direct taxes Direct taxes :

    Direct taxes: Whenever the liability to pay tax and the burden of that tax fall on similar person, it is termed as direct tax. Illustrations are: wealth tax, income tax, corporation tax, gift tax and so on.

    		•