--%>
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 : Technical change and vintage technology

    In heterodox economics, what implications does technical change and vintage technology contain for the cost structure of the business enterprise?

    		•
  • Q : Illustrate Scarcity and choice of

    Illustrate Scarcity and choice of Economic Perspective?

    		•
  • Q : Eco Quantity TR TC 0 $0.00 $10.00 1

    Quantity TR TC 0 $0.00 $10.00 1 $150.00 $30.00 2 $290.00 $50.00 3 $420.00 $80.00 4 $540.00 $120.00 5 $650.00 $170.00 6 $750.00 $230.00 7 $840.00 $300.00 8 $920.00 $

    		•
  • Q : Define Benefit Cost Ratio or

    Briefly describe the term Benefit Cost Ratio (or B/C Ratio) or Profitability Index (or PI)?

    		•
  • Q : Laffer curve & Tax rate Question: Do

    Question: Do raising tax rates necessarily raise tax revenue? What factors affect how tax revenue changes when tax rates change? Using the 'human capital' investment model,

    		•
  • Q : Circular flow model of the private

    I have a problem in economics on Circular flow model of the private sector. Please help me in the following question. The simple circular flow model of private sector doesn’t comprise: (i) Firms. (ii) Product markets. (iii) Government agencies.

    		•
  • Q : Comparative advantage in production I

    I have a problem in economics on Comparative advantage in production. Please help me in the following question. The oranges are grown in Florida and potatoes are grown in Maine mainly since: (i) orange-grower’s in Maine have not lobbied effectiv

    		•
  • Q : Summary of what can cause a decrease in

    Illustrate a summary of what can cause a decrease in demand?

    		•
  • Q : Introduction of the term combined

    Give a brief introduction of the term combined leverage? And in what manner it is calculated?

    		•
  • Q : Government Pegged Currencies Question:

    Question: If a government pegs the value of its currency to another currency, the government must stand ready to i. _________________________ the "hard" currency to defend the pegged value of its own currency. ii.

    		•