Jim Whitney Economics 250

Choosing the best feasible bundle: comparing value and cost

    The goal of consumer optimization is to allocate your income across the goods you like so as to get as much utility (well-being) as possible. This involves comparing benefits (value) and costs of alternative goods.
    Example: Suppose that last month you spent your $160 food budget on 40 health food snacks (H=goodX) at $2 each and 80 junk food snacks (J=goodY) at $1 each. With this consumption bundle you were willing to trade 3 junk food snacks for 1 health food snack. What should you do?
    a. Consume more health food and less junk food.
    b. Consume less health food and more junk food.
    c. Continue consuming your present quantities.
 
   The logic - bargain hunting:
  General case Example
Step 1: Use willingness - to - trade information to determine presonal value What size DY = What offsetting size DX? 3J = 1H
Step 2: Use price information to calculate market cost PyDY whitespace.gif (816 bytes)versus PxDX whitespace.gif (816 bytes) whitespace.gif (816 bytes) whitespace.gif (816 bytes)
Step 3: Change consumption if you can find a bargain    (1) PyDY >  PxDX: shift to more X, less Y
   (2) PyDY <  PxDX: shift to more Y, less X
   (3) PyDY =  PxDX: stay where you are		  
   The geometry: Recall that (a) MRS is the slope of your indifference curve, and (b) Px/Py is the slope of your budget line.
   So consider the geometry of the three possible "bargain hunting" outcomes:
        (1) When X is the better bargain:  PyDY >  PxDX => DY/DX (= MRS) > Px/Py -- Uo is steeper than BLo
        (2) When Y is the better bargain: PyDY <  PxDX => DY/DX (= MRS) <   Px/Py -- Uo is flatter than BLo
        (3) When you should stay where you are: PyDY =  PxDX => DY/DX (=  MRS) = Px/Py -- Uo and BLo have same slope
   The math:
   (a) MRS (=MUx/MUy) measures the relative marginal value of X compared to Y.
   (b) Px/Py measures the relative cost to you of X compared to Y.
   So in math terms:
        (1) MRS > Px/Py => relative value of X is greater than its relative cost, so consume more X and less Y
        (2) MRS < Px/Py => relative value of X is less than its relative cost, so consume less X and more Y
        (3) MRS = Px/Py => relative value of X = its relative cost, so you are doing the best you can
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    Note1: The actual amounts you have of each item typically influence the trade-off you are willing to make, but note that they are irrelevant to the actual calculation--all you need is the MRS and price information.
    Note2: As you reallocate your income, your MRS moves toward equality with Px/Py (which remains constant). If MRS>Px/Py, you consume more X and less Y which will lower your MRS as you move down your indifference curve. If MRS<Px/Py, you consme less X and more Y which will raise your MRS as you move back up your indifference curve.