emba induction session 3

8/10/2019 EMBA Induction Session 3

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Induction on

Preliminary Econometrics

Basics on the Use of Mathematics on Economics)Ace Institute of Management

Executive MBA Program

Session 3

Economic Application: Microeconomics

InstructorSandeep Basnyat

[email protected]

9841 892281
mailto:[email protected]:[email protected]


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Calculus in Managerial Economics

Marginal Applications

Marginal Product of the Labour (MPL) =Q

L

Marginal Revenue (MR) =TR

Q

TC

Q Marginal Cost (MC) =

MPLcan be obtained by finding first derivative of Q(Total Product) with respect to Total Labour.

MRis found by differentiating TRwith respect to Q

MCis found by differentiating TCwith respect to Q


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Exercise

Assume a cost function:

TC = 150Q20Q2+Q3

Find the Marginal cost for this function.

Ans:

MC =d(150Q20Q2+Q3)

dQdQ

d(TC)____=

= 15040Q + 3Q2MC


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Exercise

Given the cost function:TC = 1000 + 10Q - 0.9Q2+ 0.04Q3

Find: MC, TVC, AVC functions

TC = 1000 + 10Q - 0.9Q2+ 0.04Q3

1) MC = 10-1.8Q+ 0.12Q2

2) TVC = 10Q - 0.9Q2+ 0.04Q3

3) AVC = 10 - 0.9Q + 0.04Q2


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Suppose the Total Cost function (TC) = 500 + 20Q2

Total Revenue function (TR) = 400Q 20Q2

Find MC and MR functions.

Exercise

MR = dTR / dQ = 400 - 40QMC = dTC / dQ = 40Q


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Suppose the Total Cost function (TC) = 500 + 20Q2

Total Revenue function (TR) = 400Q

20Q2

Assume that MC and MR are equal for this firm. Howmuch quantity (Q) will be produced at that level?

Exercise

40Q = 400 - 40Q

Q = 5 units.

At, Q = 5, how much is

a) Total Revenue

b) Total Cost

c) Total Profit

d) Per unit selling Price

1000

1500

500300


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Exercise

Assume that demand function for a firm is:

P = 142Q. Find TR and MR for this firm.

TR = (142Q)Q = 14Q2Q2

MR = 144Q

Assume that the firm has constant MC = 2. At the

level where MC = MR, find total quantity produced.Q = 3

At Q = 3, find: P, TR, TC and Profit.

P = 8; TR = 24; TC = 6; Profit = 18


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Economic Applications

Profit Maximization

Revenue Maximization

Average Total Cost or Average CostMinimization

Equilibrium and disequilibrium in the

economy and its firm Changing demand and supply


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Profit Maximization

One of the most important objectives of anorganization.

Profit = Total RevenueTotal Cost

Big question:How can we maximize theoverall level of profit?

a) By charging maximum price? Or

b) By producing maximum quantity? Or

c) By producing optimum quantity?


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Profit Maximization

If increase Qby one unit,

revenue rises by MR,

cost rises by MC.

If MR> MC, then increase Qto raise profit.

If MR< MC, then reduce Qto raise profit.

What Qmaximizes the firms profit?


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Profit Maximization

505

404

303

202

101

45

33

23

15

9

$5$00

Profit =

MRMC

MCMRProfitTCTRQAt any Qwith

MR> MC,

increasing Q

raises profit.

5

7

7

5

1

$5

10

10

10

10

2

0

2

4

$6

12

10

8

6

$4$10

At any Qwith

MR< MC,

reducing Q

raises profit.

Firms maximize profit by producing the Quantity until

MR = MC


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ExerciseAssume a cost function: TC = 1000 + 2Q + 0.01Q2 and a constantmarginal revenue $10 per unit for a firm.

a) Calculate the profit maximizing output (Q); andb) Total profit if the selling price per unit (P) = MR.

Solution:

a) MC = dTC /dQ = 2+0.02QProfit maximizing output is at where

MR = MC

10 = 2+0.02Q

Therefore, Profit Maximizing Quantity (Q) = 400 units.b) Profit = TRTC = [(PxQ)TC]

= [(10x400)(1000 + 2(400) + 0.01(4002)] = $600


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ExerciseAssume the following functions for a firm

Demand : P = 7,5003.75QTotal Cost: TC = 1,012,500 + 1,500Q + 1.25Q2

Find the profit maximizing Quantity for this firm.

Q = 600 units.

At Q = 600, find:

a)Price per unitb)Total Revenue

c) Total Profit

P = 5,250TR = 3,150,000

= 787,500


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Demand : P = 20 - QTotal Revenue: TC = Q2 + 8Q + 2

Find the followings for this firm.

a)Profit maximizing Quantityb)Price per unit

c) Total Revenue

d)Total Profit

Q = 3

P = 17

= 16

TR = 51


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Demand : Q = 902PTotal Revenue: TC = Q3 - 8Q2+ 57Q +2


a)Profit maximizing Quantityb)Price per unit

c) Total Profit

Q = 4

P = 43

= 6


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1.506

2.005

2.504

3.003

3.502

1.50

2.00

2.50

3.00

3.50

$4.004.001

n.a.

9

10

10

9

7

4

$ 0$4.500

MRARTRPQ

1

0

1

2

3

$4

Sales Revenue or

Revenue Maximization

Sales

Revenue

Maximization

Condition

MR = 0


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Q = 1000 units.a)Revenue maximizing Quantity

b)Price per unit

c) Total Revenue

d)Total Profit / Loss

P = 3,750

TR = 3,750,000

= - 12,500


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Demand : P = 4,00020QTotal Cost: TC = 2000 + 400Q

Find the followings for this firm under

(a) Profit maximization objective

(b) Revenue Maximization objective.

i) Maximizing Quantity

ii) Price per unit

iii) Total Profit / Loss

Profit Revenue

90 100

2200 2000

1,60,000 1,58,000


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ExerciseAssume that you have written a new Economics textbook. Thepublisher has offered you the following contract options for

royalty payment.a) 10% of Total Revenue; or

b) 15% of Total Profit

The publishers total revenue and total cost functions are as

follows:Total revenue : TR = 10,000Q5Q2

Total Cost: TC = 10,00020Q + 5Q2

(a) If you are a profit maximizer, which contract should you

choose?(b) If you are a revenue maximizer, which contract should you

choose?


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Solution to previous exercisea) Profit Maximization case:

Royalty from 1st contract (10% of TR): 375,499.5

Royalty from 2nd contract (15% of ): 375,001.5

Decision: Choose the 1stcontract

a) Revenue Maximization case:

Royalty from 1st contract (10% of TR): 5,00,000

Royalty from 2nd contract (15% of ): 1500

Decision: Choose the 1stcontract


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Average Total Cost or Average Cost

Minimization

Related to two important costs: MC and ATC

Recall:

ATC = AFC + AVC or TC / Q

MC =TC

Q


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Marginal Cost (MC)

is the change in total cost from

producing one more unit:

Marginal Cost

6207

4806

3805

3104

26032202

1701

$1000

MCTCQ

140

100

70

50

40

50

$70

TC

Q

MC=

$0

$25

$50

$75

$100

$125

$150

$175

$200

0 1 2 3 4 5 6 7

Q

Cos

ts


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$0

$25

$50

$75

$100

$125

$150

$175

$200

0 1 2 3 4 5 6 7

Q

Cos

ts

Average Total Cost Curves

88.57

8076

77.50

86.67

110

$170

n.a.

ATC

6207

48063805

3104

2603

2202

1701

$1000

TCQ


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Important Economic Relation: ATC and MC

ATC

MC

$0

$25

$50

$75

$100

$125

$150

$175

$200

0 1 2 3 4 5 6 7

Q

Cos

ts

When MCATC,

ATCis rising.

The MCcurve crosses theATCcurve at

theATCcurves minimum.

ATC is minimum where,

ATC = MC

AVC is minimum where,

AVC = MC


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Exercise

Given the cost function:

TC = 1000 + 10Q - 0.9Q2+ 0.04Q3

Find:

1) MC, TVC, AVC functions (equations)2) Find Q when AVC is minimum.


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Worked out SolutionTC = 1000 + 10Q - 0.9Q2+ 0.04Q3

1) MC = TC / Q = d(TC) / dQ

= 10-1.8Q+ 0.12Q2

2) TVC = TCTFC

= 1000 + 10Q - 0.9Q2+ 0.04Q31000

= 10Q - 0.9Q2+ 0.04Q3

3) AVC = TVC / Q =(10Q - 0.9Q2+ 0.04Q3)/Q

= 10 - 0.9Q + 0.04Q2

4) Q at Minimum AVC is:

AVC = MC

10 - 0.9Q + 0.04Q2 = 10-1.8Q+ 0.12Q2

Or, - 0.08Q2 + 0.9Q = 0

Or, Q(- 0.08Q+ 0.9) = 0

Or, Q =0 and - 0.08Q+ 0.9 = 0 i.e, Q = 11.25 (Minimum AVC)


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Find the followings for this firm if your objective is

to minimize average cost.a) Q

b) Price per unit

c) Total Revenued) Total Profit

P = 4,125

TR = 3,712,500= 337,500

Q = 900


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Thank You

emba induction session 3

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