--%>
Assignment Help - homework help

Demand curve for peanuts

Question:

a) Johnny consumes peanuts (x1) and a composite good (x2). His utility function is U = x1x2. His marginal utilities are MU1 = x2 and MU2 = x1. Johnny's budget is $20 and the price of the composite good is $1. Derive Johnny's demand function for peanuts.

b) Ambrose consumes peanuts (x1) and a composite good (x2).He has a utility functionU = 4 x1 + x2. This means his MU1 = 2/√x1 and his MU2 = 1 . The price of the composite good is p2 = 1. His budget is $20 per month. Derive Ambrose's demand function for peanuts. How does it compare with Johnny's demand curve for peanuts?

Solution:

a) U = x1x2

MRS = MU1/MU2 = x2/x1

Now, MRS = P1/P2 = P/1 = x2/x1 => x2 = 2Px1 {taking P1 = P}

Putting this value in budget equation:

Px1 + x2 = 20

  1.   Px1 + 2Px1 = 30
  2.   Px1 = 10
  3.   x1 = 10/P
  4.   x2 = 20

b) U = 4 Öx1 + x2.

MRS = MU1/ MU2 = (2/Öx1)/1 = 2/Öx1

Now, MRS = P1/P2 = P/1 = 2/Öx1

  1.   Öx1=2/P
  2.   x1 = 4/P2

Therefore, Ambrose's demand for peanuts does not depend upon his income, while Johnny's demand for peanuts does depend upon his income.

   Related Questions in Microeconomics

  • Q : Risk and Uncertainty of Probability

    If estimating the nature of a probability function for an event entails considerable guesswork since experience along with the event is more sporadic or rare which any estimates are extremely speculative, in that case we confront a concept Fra

    		•
  • Q : Price elasticity of demand among

    The price elasticity of demand as in below illustrated figure for DVD games among prices of $20 and $30 is about: (w) 1.00. (x) 25. (y) 1/25. (z) 1/2.

    Q : Influences of Ceteris Paribus The Latin

    The Latin phrase applies to the idea which all other effects on some dependent variable are to be supposed constant if examining the effect of changing a single independent variable is as: (1) Fiat justitia, ruat coelum. (2) Platea unum. (3) Unum paribus. (4) Ceteris

    		•
  • Q : Tax on a good tends to make The tax on

    The tax on a good tends to make: (i) Inflationary pressure the govt. can disperse by cutting its spending. (ii) The wedge among prices buyers pay and the prices sellers obtain. (iii) Rises in supply from the viewpoint of buyers. (iv) More quick transa

    		•
  • Q : Comparative advantage in making food

    When Wilma can make a brontosaurus burger in 10 min and a cactus cooler in 5, whereas Betty can make the burger in 8 min and the cactus cooler in 3. Then find out the right option from the above: (1) Betty consists of a comparative disadvantage in the coolers and a co

    		•
  • 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 : Capital Labor Ratios and Income Assume

    Assume that half of the world population, randomly certain, was magically vaporized through space aliens, although no other aspect of life onto Earth was influenced. Ignoring any psychological trauma that calamity might entail, upon average, the economic

  • Q : Problem on change in preferences Can

    Can someone help me in finding out the right answer from the given options. Tim liked to snack on slim jims on fishing; however his friend Earl for all time brought beef jerky. Tom slowly developed a taste for jerky and at present buys it more frequently than slim jim

    		•
  • Q : Impact of deficient demand in an economy

    Describe deficient demand in an economy? Determine its impact on output, employment and price? Answer: Deficient demand terms to the condition when aggregate demand

    		•
  • Q : Maximizes profit for output HoloIMAGine

    HoloIMAGine has patented a holographic technology which creates 3-D photography obtainable to consumers. It maximizes profit at: (i) output q1. (ii) output q2. (iii) output q3. (iv) output q4. (v) output q5.

    		•