--%>
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 : Relationship between Total utility and

    Describe the relationship between Total utility (TU) and Marginal utility (MU)? Answer:

    Q : When Shortages occur Shortages take

    Shortages take place whenever the market price: (1) Most greatly surpasses the average person’s demand price. (2) Is above the usual seller’s supply price. (3) Equivalents production costs plus the maximum possible gain. (4) Lies beneath t

    		•
  • Q : Uncertainty and Decision-making I have

    I have a problem in economics on Uncertainty and Decision-making. Please help me in the following question. The error of omission would be: (i) The failure of an individual to invest in Microsoft 20 years ago. (ii) Individual cheating on a test. (iii)

    		•
  • Q : Increase in Income Tax Progressivity

    When this figure demonstrated Lorenz curves for distribution of income after taxes and transfers, in that case it is UNTRUE of the Lorenz curves demonstrated in this demonstrated figure that: (1) line 0E0' represents a Lorenz curve of

    		•
  • Q : Determine a price taker from firm Of

    Of the given firms, the probably to be a price taker would be a: (i) sheep herder in a remote part of New Zealand. (ii) local gas and electric company. (iii) sculptor’s agent who contacts potential buyers through the internet. (iv) small town&rs

    		•
  • Q : Determine slope of demand for given

    For edcah $.10 per gallon hike within gasoline prices, Ima Driver cuts her monthly consumption of gasoline with 5 gallons. There slope of her demand for gasoline: (w) 1/2 when the change in price is expressed within cents, and 500 when the change in p

    		•
  • Q : Twenty-one amendment of public polices

    Drive-by shootings by that several groups of beer or liquor distributors or producer attempted to liquidate rival groups largely finished while the: (w) U.S. Constitution was ratified and Whiskey Rebellion which began into 1794 finally finished. (x) 21st amendment to

    		•
  • Q : Distribution of income in a purely

    For a specified distribution of income within a purely competitive economy, marginal social benefit will the same marginal social cost unless: (w) “hit and run” entrepreneurs prosper. (x) economic profits

    		•
  • Q : Structure-conduct-performance From

    From roughly 1890 till 1970 year, the “structure-conduct-performance paradigm” controlled theories regarding how firms behave in various types of markets. The term “structure” in this expression refers to such

    		•
  • Q : Economic losses driven down to zero

    Exit by a competitive industry will arise till economic: (1) profits are driven to zero. (2) profits counterbalance accounting losses. (3) incomes are equalized for comparable workers. (4) costs are sufficiently below accounting losses. (5) losses are driven down to z

    		•