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Incremental and Average Slopes

Incremental and Average Slopes. Ted Mitchell. Q = ???A. Q = Quantity sold. x x. x x. x x x. x. x. x x x. x x x. x x. x. x. x. A = Advertising Budget. Q = kA a. Q = Quantity sold. x x. x x. x x x. x. x. x x x. x x x. x x. x. x.

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Incremental and Average Slopes

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  1. Incremental and Average Slopes Ted Mitchell

  2. Q = ???A Q = Quantity sold x x x x x x x x x x x x x x x x x x x x A = Advertising Budget

  3. Q = kAa Q = Quantity sold x x x x x x x x x x x x x x x x x x x x A = Advertising Budget

  4. Increase in Volume Quantity Sold Q = kAa Q A Advertising Budget

  5. Increase in Volume Quantity Sold Q = kAa Q Q = (Q/A) x A Q/A is the average rate that sales increase for $1 increase in advertising budget A Advertising Budget

  6. Increase in Revenue Revenue R = PQ =PkAa R = (R/A) x A R/A average increase in Revenue for a $1 increase in advertising budget A Advertising Budget

  7. What Does The Profit Curve Look Like? Profit M* 0 A* Advertising

  8. What Does The Profit Curve Look Like? Z = (Z/A) x A Z/A = the average rate at which the profit increases for a $1 increase in advertising budget Profit Zm* 0 A* Advertising

  9. What is the difference between average response and the marginal or incremental response?

  10. Three Slopes Slope of the arc dZ/dA = Slope at a point Profit Z/A =Average Slope 0 Optimal Advertising Advertising

  11. Return on Advertising Expense is always falling as Advertising Increases Profit Z 0 Z = ROAE x Advertising Z = (Z/A) x A Advertising

  12. It is better to use the incremental change rather than the average rate • But changes in averages are harder

  13. You walked from home to school at an average pace of 10 miles per hour • You walked from school to home at an average pace of 5 miles per hour • What was your average pace for the round trip?

  14. You walked from home to school at an average pace of 10 miles per hour • You walked from school to home at an average pace of 5 miles per hour • What was your average pace for the round trip? • Not (10 + 5)/2 = 7.5 miles per hour!!! • Assume the distance was 100 miles • At 10 mph it took 100/10 = 10 hours • At 5 mph it took 100/5 = 20 hours • You walked 200 miles in 30 hours and your average speed was 200/30 = 6.666 mph

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