--%>
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 : Enterprise is dictated primarily by

    “The legal form an enterprise assumes is dictated primarily by the financial requirements of its particular line of production.”  Do you agree?

    		•
  • Q : Market Apparent program For the

    For the question below, utilize the given information. The market for gizmos is competitive, with an increasing sloping supply curve and a downward sloping demand curve. With no govt. intervention, the equilibrium price is $25 and the equilibrium quantity is 10,000 gi

    		•
  • Q : Describe double coincidence of wants

    Double coincidence of wants: This means that one person's wishing to buy and sell should coincide with another person’s wish to buy and sell.

    		•
  • Q : Conception of the Invisible Hand by

    Conception of the “Invisible Hand” by Adam Smith relies on mechanisms like those as underpin: (1) William Stanley Jevons’ “sunspot” theory of business cycles. (2) the biological concept of Homeostasis. (3

    		•
  • Q : Determine the monetary prices while

    Dividing monetary prices from each other yields: (v) nominal prices. (w) relative prices. (x) subjective prices. (y) absolute prices. (z) transaction prices. Hello guys I want your advice. Please recommend some vie

    		•
  • Q : Problem related to market circular flows

    In output markets, the simple circular flow model, households replace their _________ for _________. Can someone help me in determining the right answer from the given options. (1) Resources | income. (2) Labor | g

    		•
  • Q : Equilibrium market rate & Undervalued

    Question: a. In the short-run, it is easier for a country to maintain a peg that undervalues a currency (relative to the equilibrium market rate) than it is to maintain a peg that overvalues the currency (relative

    		•
  • Q : Introduction of the term net present

    Give a brief introduction of the term net present value? Write down its admittable rules, their merits and demerits?

    		•
  • Q : Tax revenues to reduce rate of inflation

    Explain how government might manipulate its expenditures and tax revenues to reduce rate of inflation?

    		•
  • Q : Micro economics and macro economics

    Micro economics and macro economics:Economic theory can be widely divided into micro and macroeconomics. The word micro means small and macro means big.In microeconomics, we deal

    		•