--%>
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 : Occurrence of increase in supply in

    In short run, the increase in supply takes place whenever the: (1) Supply curve shifts upward and to left. (2) Preferences of consumers change in a positive direction. (3) Market price raise. (4) Amounts producers make accessible rise at each and every price. (5) Publ

    		•
  • Q : Proprietorships and Partnerships The

    The advantage of a partnership is: (i) Its ease of organization as compared to the corporation. (ii) Its limited liability. (iii) Its capability to outlive the partner’s death. (iv) The lack of divergences. C

    		•
  • Q : Normal accounting returns to investment

    Pure economic profits do not arise due to: (w) monopoly power. (x) capital owners’ receipts of normal accounting returns to investment. (y) risk and uncertainty. (z) entrepreneurial innovation. How can I solv

    		•
  • Q : Determinants that consumers want to buy

    In addition to price, what are the other determinants that consumers want to buy?

    		•
  • Q : How is Economic policy more scientific

    Which of the given LEAST describes the widespread but erroneous view which economists seldom agree: (1) The media focuses upon controversy, not agreement. (2) Political considerations, more than economic logic, find out policies. (3) Some economists may feel obligated

    		•
  • Q : Constant cost industries In

    In constant-cost, the purely competitive industries: (w) total cost is constant at every output. (x) marginal cost is constant at each output. (y) number of firms is constant at every output. (z) long-run supply price is uninfluenced by output. <

    		•
  • Q : Possible elasticity of brain power of TV

    When doubling your viewing of soap operas to sixteen hours per week causes your IQ score to reduce from a genius level of 140 to a sluggish 70, your TV elasticity of brain power is possibly: (i) -1.0. (ii) +1.0. (iii) -2.0. (iv) 2.0. (v) -0.5.

    Q : Problem Based on Economic Rent Location

    Location or site rents are as: (w) unrelated to the geographic location of a firm in a market. (x) determined from the fertility of land. (y) generated while a firm’s location allows this to charge more for its output or to pay less for its inpu

    		•
  • Q : Competitive Prices for selling This

    This purely-competitive producer’s generic bricks presently sell for: (i) $60 per thousand. (ii) $70 per thousand. (iii) $80 per thousand. (iv) $90 per thousand. (v) $100 per thousand.

    Q : Consequences of rise in union wages Can

    Can someone help me in finding out the right answer from the given options. The possible consequences of a rise in union wages comprise reduced: (1) Union employment and a refusal in non-union wages. (2) Shares of national income to the labor however growth of union e

    		•