--%>
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 : Problem on Substitute Goods Can someone

    Can someone help me in finding out the right answer from the given options. The substitute goods are: (i) Usually consumed altogether. (ii) Inferior to luxury goods. (iii) Generally free goods. (iv) Replacements for each other.

    Q : Illustration of Substitution Effect

    Sally is very rich that money hardly matters to her, although when the price of JIF chunky peanut butter doubled Sally switched to Peter Pan chunky peanut butter. This alters is an example of the: (1) Income effect. (2) Payback effect. (3) Substitution effect. (4) Pri

    		•
  • Q : Jeremy Bentham utilitarianism Possible

    Possible utilization of a ‘felicific calculation’ to recognize punishments for the crimes was derived from: (1) Medieval scholasticism. (2) Say’s Law. (3) Gresham’s Law. (4) Marshall’s Maxim. (5) Jeremy Bentham&r

    		•
  • Q : Define deficit budget Deficit budget :

    Deficit budget: When expenditure of the government is greater than its receipts, it is termed as deficit budget.

    		•
  • Q : Can GNP be more than GDP Can GNP be

    Can GNP be more than GDP? Answer: Yes, GNP can be greater or more than GDP if NFIA is positive.

    		•
  • Q : Average revenue and marginal revenue

    In spite of of the amount sold, price equals for a price-taker firm on both average: (i) revenue and marginal revenue. (ii) variable cost and marginal cost. (iii) fixed cost and average variable cost. (iv) total cost and marginal revenue.

  • Q : Lower rates of return by financial

    Financial assets will create lower rates of return to prospective investors while: (w) they become more liquid. (x) their prices go up. (y) interest rates increase. (z) default risks decrease. Hey

    		•
  • Q : Problem on competitive resource market

    The firm in a perfectly competitive resource market which consists of market (monopoly) power in its output market will hire the resources to a point where: (1) w = MRP. (2) VMP = MRP. (3) w = VMP. (4) MFC = w. Can someone please h

    		•
  • Q : Major disadvantage of operating a

    One of the main disadvantages of operating a corporation in relative to operating a sole partnership or proprietorship is that corporations tend to: (i) Offer just limited legal liability to their stockholders. (ii) Utilize specialized management pers

    		•
  • Q : Unregulated monopoly economic efficiency

    Mainly economists object to unregulated monopoly primarily since: (w) economies of large scale operation may be attained. (x) technological advance may be fostered. (y) economic efficiency would be promoted. (z) economic efficiency may be decreased.

    		•