Managerial Economics

1
Simple maxim of marginal analysis Make a
small move to a nearby alternative if and only
if the move will improve ones objective. Keep
moving, always in the direction of an improved
objective, and stop when no further move helps.
Expand an Activity if and only if the Extra
Benefit exceeds the Extra Cost.
2
Refresher Differential Calculus

• A derivative is a rate of change (marginal
  change, slope).
• From total cost, the first derivative gives
  marginal cost (slope at specific point).

3
Refresher Differential Calculus
Rule 1 The derivative of a constant is zero.
Where c is a constant
4
Refresher Differential Calculus
Rule 2 Power rule
(x3)3x2
(xn)nxn-1
(5x2)10x
(.5x4)2x3
5
THE FIRMS BASIC PROFITMAXIMIZATION PROBLEM

• What Quantity of Output should the Firm
• Produce and Sell and at What Price?
• Firm produces single good for single market.
  Objective profit max.
• Must determine quantity and price of good.
• Assume firm can predict revenue and cost
  consequences of price and output decisions with
  certainty.

6
MAXIMIZING PROFIT FROM MICROCHIPS
F2
Demand equation Q 8.5 - .05P
Write profit as ? Revenue - Cost
Price ( 000)
Inverse demand equation P 170 - 20Q
170 130 90 50
Revenue function Rev P x Q R (170-20Q)Q
170Q-20Q2
Quantity in Lots
0 2 4
6 8
7
Example Q 425-1.25P
Find inverse demand function Q 425-1.25P 1.25P
425-Q P 340 - .8Q
Find revenue function R PQ R (340-.8Q)Q R
340Q - .8Q2
8
THE FIRMS OPTIMAL OUTPUT DECISION
Profit Max Output where MR MC.
R, C ?
C 100 38Q Fixed costs 100 Var costs
38/unit
300 200 100 0 -100
R 170Q - 20Q2
M? 0
Profit Function ? (170Q - 20Q2)-(100 38Q)
-100 132Q 20Q2
Q
0 2 4
6 8
3.3
9
MAXIMIZING PROFIT USING MARGINAL GRAPHS
Set MR MC.
170
P
Demand
MC
38
MR
Q
10
MAXIMIZING PROFITMATH SOLUTIONS

• Start with Demand and Cost Information
• P 170 - 20Q and C 100 38Q

• Therefore, R 170Q - 20Q2
• so MR 170 - 40Q and MC 38

• Setting MR MC implies 170 - 40Q 38
• or 132 40Q

Q 132/40 3.3 lots
P 170 - (20)(3.3) 104 K
? 343.2 - 225.4 117.8
11
SENSITIVITY ANALYSIS
Considers changes in Fixed Costs, Marginal
costs, or
Demand Conditions
170
A change in fixed cost has no effect on Q or P
(because MR and MC are not affected).
P
Demand
MC
38
Q
12
SENSITIVITY ANALYSIS
Considers changes in Fixed Costs, Marginal
costs, or
Demand Conditions
170
An increase in MC implies a fall in Q and an
increase in P.
Demand
MC
MC
38
Q
Q
13
SENSITIVITY ANALYSIS
Considers changes in Fixed Costs, Marginal
costs, or
Demand Conditions
Finally, consider a change in Demand Conditions.
170
P
Shift in Demand
MC
38