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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.

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).

Refresher Differential Calculus

Rule 1 The derivative of a constant is zero.

Where c is a constant

Refresher Differential Calculus

Rule 2 Power rule

(x3)3x2

(xn)nxn-1

(5x2)10x

(.5x4)2x3

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.

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

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

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

MAXIMIZING PROFIT USING MARGINAL GRAPHS

Set MR MC.

170

P

Demand

MC

38

MR

Q

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

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

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

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

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