--%>
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 : Pure economic profit on rate of return

    Owners of corporate stock obtain pure economic profit only to the extent which the rates of return realized by owning the stock exceed the: (1) interest rate that would have been produced by other investments entailin

    		•
  • Q : Profit maximizing strategy at breakeven

    Nostalgia Corporation would exactly break-even on its Silver Screen DVDs when, in place of correctly identifying its profit maximizing strategy, this: (w) operated at point i, charging only $10 per DVD and producing 8 million DVD. (x)

    		•
  • Q : Short-run supply curve and marginal

    Short-run supply curve of a purely competitive firm’s is the positively sloped part of the marginal cost curve which is above its: (w) average fixed cost curve. (x) resource demand curve. (y) average variable cost. (z) short-run

    		•
  • Q : Determine least price elastic points

    The section of this supply curve for 2×4s which is least price elastic is in between: (i) point a and point b. (ii) point b and point c. (iii) point c and point d. (iv) point d and point e. (v) point e and point f.

    Q : Market power conduct by a price maker

    HoloIMAGine has patented a holographic technology which makes 3-D photography obtainable to consumers. The illustrated figure shows such that HoloIMAGine: (1) makes profit equal to area dcP0P3 since this can price discriminate perfectly. (2) has market power as a pric

    		•
  • Q : Effects of Globalization On Indian

    On Indian industry what are the effects of globalization?

    		•
  • Q : Law of diminishing returns for a good

    The point is inevitably reached where an individual derives less extra enjoyment from the extra units of any good. This is mainly well-suited with: (i) Supply curves that slope-up and to right. (ii) Concave (or bowed out) production possibilities frontiers. (iii) The

    		•
  • Q : .. Within a graph along with output on

    Within a graph along with output on the horizontal axis and whole revenue on the vertical axis, determine the shape of the total revenue curve for a perfectly competitive seller: w) U-shaped. x) inverted U-shaped. y) a horizontal line. z) a ray from the origin.

    		•
  • Q : Unemployment Select right answer for

    Select right answer for Unemployment: A) causes the production possibilities curve to shift outward. B) can exist at any point on a production possibilities curve. C) is illustrated by a point outside the production possibilities curve. D) is illustra

    		•
  • Q : Distribution of Income before taxes and

    Income is distributed before taxes and transfers in the United States such as, in 2003 year, the lowest quintile [20%] earned around: (w) 4% of all income and the highest quintile earned over half of all income. (x) 5% as much as the highest quintile.

    		•