Jim Whitney Economics 102

  Toolkit of common functions in economics

1.  Linear functions: Y = B0 + B1X
  
Common applications:  
          Linear demand (always: B1 < 0) 
          Linear supply (usually: B1 > 0) 
          Consumption (0 < B1 < 1) 
          Savings (savings B1 = 1 - consumption B1) 
          Total revenue for a price-taking firm (B0 = 0; B1 > 0)
  
Distinguishing characteristic: Constant slope
  
Warning: As noted in your text, for demand and supply we commonly make the y-axis variable (Price) the independent variable and the x-axis variable (Quantity) the dependent variable: Q =  B0  + B1 P. In math terms, note that B0 is then the x-axis intercept and B1 is the reciprocal of the slope. It's just a convention, but there are sensible interpretations to either way of writing the equation, depending on the situation. 
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whitespace.gif (816 bytes)
2. Polynomial functions:  Y = B0 + B1 X + B2 X2 + B3 X3
                        linear:  Y = B0 + B1 X
                  quadratic: Y = B0 + B1 X + B2 X2
                         cubic: Y = B0 + B1 X + B2 X2 + B3 X3
 

Common applications:  
          Linear (see above; note that linear functions are actually a subset of polynomials) 
          Quadratic: Production possibilities curve (B2 < 0) 
                             Total revenue for a firm facing linear demand (B0 = 0; B1 > 0; B2 < 0) 
          Cubic: Production (often: B0 = 0; B1 > 0; B2 > 0; B3 < 0) 
                       Cost (often: B0 > 0; B1 > 0; B2 < 0; B3 > 0)
  
Distinguishing characteristics: Size of slope can vary. Behavior of slope can change: slope can turn from positive to negative, or can get steeper for awhile, then get flatter
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whitespace.gif (816 bytes)
3. Power functions: Y = B0 XB1 
  
 Common applications: (all with B0 > 0) 
           Cost (B1 > 1) 
           Production (0 < B1 < 1) 
           Utility (0 < B1 < 1) 
           Demand (B1 < 0)
  
 Distinguishing characteristic: slope can vary in size but never changes its sign