Marginal analysis

Marginal revenue,

Elasticity

Price elasticity of demand:

E = %d_q / %d_p.

Income Elasticity of demand:

E = %d_q / %d_i.

Negative, means inferior good. Generic cereal, with more money, less generic cereal.

Imagine the gov. says the income will increase 5% then my delta q will increase 2.5%, given an elasticity of .5.

  • Normal good. Positive
  • Inferior good. Negative.

How responsive are customers to change of income.

Cross price elasticity of demand (the price of a related good):

E = %d_q / %d_Pr    where Pr is the price of a related good
  • Negative: Complementary.
  • Positive: Substitute.

Related goods can be of two types:

  • Substitute of your product (McDonalds vs BurgerKing)
  • Complementary (Tennis rackets vs Tennis balls)

Any variable in the : Q = a + bP + cN + dI + cR can give us an elasticity.

Set elasticity == -1 or using marginal analysis, take the derivative and equal the equation to zero.

What is the price P* that will maximize revenue:

max Total revenue.

Derivative in is called marginal revenue.

TR -> MR = 0

Given : Q = 1124.43 - 1.617P Solve for P in terms of Q ` p = 695.72 - 1/1.617 Q`

TR = ((695.72 - 1/1.617 Q) Q)
TR = 695.72Q - 1/1.617 Q^2 (take the derivative)
MR = 695.72 - 2/1.617Q = 0 and now we can solve for the optimal Q
2/1.627Q = 695.72
Q = 562.21

Optimal quantity is going to be 562.21, now we can use it in the price equation and the price will be $347.34. This the optimal price to charge. The total revenue, price times quantity. Price elasticity of demand at this point will be -1.

 E = -1.617 x 347 / 562.21 = -1

This is when the revenue is maximized.