--%>
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 : When is Price Ceiling not create

    Price ceilings do NOT create pressures for: (w) shortages of price controlled goods. (x) black markets, queuing, or sales by favoritism. (y) opportunity costs to be lower than or else. (z) transactions at monetary prices below the equilibrium price.

    		•
  • Q : Devaluation and depreciation of

    Distinguish among devaluation and depreciation of domestic currency

    		•
  • Q : Monopoly market structure When one firm

    When one firm controls all production and the price of a good without shut substitutes, there is: (i) monopoly market structure. (ii) violation of the law of demand and supply. (iii) lack of equity although assurance of efficiency. (iv) legal barrier to entry. (v) cer

    		•
  • Q : Power monopsonist I have a problem in

    I have a problem in economics on Power of monopsonist. Please help me in the given question. The firm which is the sole buyer of a specific good or resource is a: (m) Monopsonist. (n) Plutocracy. (o) Bilateral monopolist. (p) Price discriminator. (q) Conglomerate.

    		•
  • Q : Severe Poverty of Demography From the

    From the 1950 year, severe poverty has declined most sharply in between people while they experience: (w) low levels of education. (x) discrimination in employment. (y) old age. (z) poor health. Can someone explain

    		•
  • Q : Help The problem of asymmetric

    The problem of asymmetric information is that: a) neither health care buyers nor providers are well-informed. b) health care providers are well-informed, but buyers are not. c) the outcomes of many complex medical procedures cannot be predicted. d) insurance companies are well-informed

    		•
  • Q : Oligopolistic nature of industries The

    The oligopolistic nature of several industries is probably to be attributable to: (1) overly expansionary macroeconomic policies. (2) corporate instability. (3) economies of scale. (4) cooperative gaming. (5) unstable Nash equilibrium.

    Q : What is Average Fixed Cost or AFC What

    What is Average Fixed Cost. Also provide its formula?

    		•
  • Q : Characteristics of pure monopoly This

    This is untrue that a firm which is a pure monopoly: (1) commonly engages in extensive advertising to differentiate its products. (2) produces a level of output which is closer to socially optimal when this price discriminates. (3) is the sole produce

    		•
  • Q : Experiencing Absolute Poverty When the

    When the minimum amounts of food, clothing and shelter essential for survival absorb all of a family’s income, in that case the family is experiencing: (w) relative poverty. (x) economic shock. (y) financial destitution. (z) absolute poverty.

    		•