--%>
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 : Elucidate redistribution of income

    Elucidate redistribution of income?

    		•
  • Q : What is an Economic Territory Economic

    Economic Territory: This refers to the region of a country where there is a free movement of goods, capital and human resources.

    		•
  • Q : Initial systematic and popular

    The initial systematic and popular description of capitalism was explained in: (1) Sir Thomas Mun’s England’s Treasure by Foreign Trade. (2) Joseph A. Schumpeter’s Capitalism, Socialism, and Democracy. (3) John Maynard Keynes’

    		•
  • Q : How can we calculate EPS How can we

    How can we calculate EPS?

    		•
  • Q : Categorization of economists for buying

    Assume that you bought a ton of gold in Santiago, and Chile for $450 per ounce and immediately sold all of this in Antwerp, Belgium for $480 per ounce. Therefore economists would categorize your movement as: (i) arbitrage. (ii) scalping. (iii) screening. (iv) speculat

    		•
  • Q : Illustrate Scarcity and choice of

    Illustrate Scarcity and choice of Economic Perspective?

    		•
  • Q : Distinguish clearly between a plant

    Distinguish clearly between a plant, a firm, and an industry?

    		•
  • Q : Determine the clearest illustration of

    The clearest illustration of economic inefficiency would be: (w) maintaining a warehouse full of pet rocks within hopes such that someday the fad will return. (x) pet rocks being unavailable to people willing to pay a price that exceeds the marginal s

    		•
  • 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 : Analysis of US GDP and GDP growth rate

    You may use a calculator and MINITAB to conduct the necessary calculations for all questions.  Analysis of US GDP and GDP growth rate (1959-2004). The following variables can be retrieved from MIN

    		•