--%>
Assignment Help - homework help

Marginal rate of substitution

Problem:

Luke likes to consumer CDs (good1) and pizzas (good 2). His preference over both goods is given by the utility function

U(x1; x2) = x21 x42.

If Luke allocates $200 to spend on both goods and if a case of CDs costs $20 and a pizza costs $10, how many cases of CDs and pizzas would he consume in order to maximize his utility subject to his income. Show your work and illustrate your answer graphically.

Summary:

The problem in economics in price theory deals with deriving maximum marginal utility and marginal rate of substitution.

Answer:

U(x1, x2) = x12x24

P1 = 20, P2 = 10

MUx1 = 2x1x24

MUx2 = 4x12x23

Therefore, MRS = ½(x2/x1)

Now, for optimization, MRS = P1/P2 = 20/10 = 2

Now, ½(x2/x1) = 2

x2 = 4x1

Putting this value into the budget equation:

20x1 + 10x2 = 200

20x1 + 40x1 = 200

x1 = 10/3

and x2 = 40/3

678_marginal rate of substitution.png

   Related Questions in Business Economics

  • Q : Market structure and pricing decision

    Just need help to see if I am in the right direction if there any think wrong need help with it.

    		•
  • Q : Public Sector Government Role

    Illustrate the Public Sector Government’s Role of providing the legal structure?

    		•
  • Q : External factors which influencing the

    Write down the external factors which influencing the capital structure?

    		•
  • Q : Positive task of speculators in market

    A positive responsibility played through speculators within a market economy is to: (1) find out price levels for entrepreneurs. (2) predict the quantity at that long run equilibrium would be attained. (3) inform government organizations of consumer p

    		•
  • Q : Advantages rising from division of

    Adam Smith known three advantages rising from divisions of labor which would lead to greater economic wealth that did not include the concept that the division of labor: (w) helps every worker refine specialized skill

    		•
  • Q : What are the main sources of growth

    What are the main sources of growth?

    		•
  • Q : Define the for whom query in market

    The market system responses the “for whom?” query with: (i) distributing goods on the basis of require. (ii) using central planning to coordinate production decisions. (iii) catering to consumers with adequate resources to demand goods. (i

    		•
  • Q : Strategic behaviour of decisionmaker If

    If one decisionmaker in interdependent circumstances calibrates its decisions to the anticipated reactions of the other party, in that case the decisionmaker is engaged within: (1) psychological forecasting. (2) profit maximization. (3) collusion. (4) strategic behavi

    		•
  • Q : Describe the Functional distribution of

    Describe the Functional distribution of income?

    		•
  • Q : Parking meters may yield little or no

    Explain: “Even though parking meters may yield little or no net revenue, because of the rationing function they perform nevertheless be retained”

    		•