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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
Sandeep_basnyat@yahoo.com
9841 892281
mailto:Sandeep_basnyat@yahoo.commailto:Sandeep_basnyat@yahoo.com8/10/2019 EMBA Induction Session 3
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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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ExerciseAssume the following functions for a firm
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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ExerciseAssume the following functions for a firm
Demand : Q = 902PTotal Revenue: TC = Q3 - 8Q2+ 57Q +2
Find the followings for this firm.
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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ExerciseAssume the following functions for a firm
Demand : P = 7,5003.75QTotal Cost: TC = 1,012,500 + 1,500Q + 1.25Q2
Find the followings for this firm.
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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ExerciseAssume the following functions for a firm
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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ExerciseAssume the following functions for a firm
Demand : P = 7,5003.75QTotal Cost: TC = 1,012,500 + 1,500Q + 1.25Q2
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
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