CPR-no: 14th January 2013 Managerial Economics Mid-term
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Question 1:
The market equilibrium can be found by setting demand = supply
20-0,00001QD=5+0,000005QS
15 =0,000015Q
Q = 1000000
P= 20-0,00001*1000000 = 10
Question 2:
The price equilibrium at this point can be calculated with by help of the point-slope method for price
elasticity of demand and plotting in the known values:
E = (10/1000000)*(1/-0,00001) = -1
The elasticity at this point is unit-elastic meaning that a one percent decrease in price will lead to a one
percent increase in quantity demanded and a one percent increase in price will lead to a one percent
decrease in quantity demanded. The price elasticity of demand is -1 in the middle of the demand curve,
and it is also here where Total Revenue is maximized, which is true when operating under perfect
competition.
Question 3:
Since it is a perfectly competitive market suppliers are price-takers, and therefore must deliver a certain
quantity at the market-price (which is P=10=MR=D). We know that the optimality condition is MR = MC
under all forms of market structure, therefore, we simply set the market price P=MR=10 equal to
BeefBrazz’ Marginal Cost function:
10 = 5 + 0,00001Q2
Solving for Q we get two solutions: Q = -707,107 or Q= 707,107
Since they cannot produce a negative output they will produce an output of Q = 707,107
CPR-no: 14th January 2013 Managerial Economics Mid-term
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Question 4:
Average Variable Cost (AVC) = Total Variable Cost / Q
Total Variable Cost (TVC) = integrate(MC)
TVC = Integrate (MC) = ∫
AVC = TVC/Q = 0,000003Q2+5
We find the value at the optimum-price we found in question 3 (707,107) by inserting it into AVC:
AVC = 0,000003*707,107^2+5 = 6,5
This is the average cost of producing each unit of Q since we don’t have TC we cannot know whether there
are any fixed costs. Assuming there are no fixed costs BeefBrazz will be making a profit since the cost of
producing is lower than the selling price.
Question 5:
CPR-no: 14th January 2013 Managerial Economics Mid-term
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Since it is a perfectly competitive market, entry barriers are low, and more suppliers will enter the market
driving the profits down to zero in the long run. This means that in the long run ATC will be equal to the
market-price, meaning that all the firms earn no profit in the long-run, as depicted in the graph below:
Question 6:
We can determine the demand function simply by using the formula for finding a straight with two points
given:
The two points are (0, 30) and (100, 25)
To find the slope (a) of a linear function: 𝑎= (𝑦2−𝑦1)/(𝑥2−𝑥1 )
The intercept with the y-axis is given (b = 30)
Inserting the values into the slope-formula we get a = -0,05
P = 30 – 0,05Q
TR = P * Q = 30Q – 0,05Q2
MR = d(TR)/d(Q) = 30 – 0,1Q
Question 7:
Given: P = -0.05 *Q + 30
MR = -0.1 *Q + 30
CPR-no: 14th January 2013 Managerial Economics Mid-term
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MC = 0.07 *Q + 7
MR = MC at optimum
-0.1 *Q + 30 = 0.07 *Q + 7
Solving for Q = 135.294118
P = -0,05*135,29+30 =
23.24
Find MR in optimum MR =
16.47
TR (P*Q) =
3,143.60
TVC =
∫
TVC=0,035*135,292+7*135,29 =
1,587.72
Profit (TR-TVC-TFC) =
1,555.88 -FC
CPR-no: 14th January 2013 Managerial Economics Mid-term
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Question 8:
Point Income elasticity is defined as the percentage change in demand because of a 1 % increase in
income.
The effect of an income change on the demand for a good. Where price elasticity related to the demand
curve, income elasticity relates to the engel curve.
𝑦
0
10
20
30
40
50
60
0 100 200 300 400 500 600 700
P MR
MC
CPR-no: 14th January 2013 Managerial Economics Mid-term
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𝑥 𝑦
Normally food is considered a necessity good, with little changes in quantity demand when price is
changed. However, since BeefBrazz produces beef it is likely that they produce various types of meat that
experience different income elasticities according to the quality of the meat. For instance, ground meat
has different fat percentages; in a hamburger the fat perce
ntage is likely to be high, and since the consumer is likely to switch to a less fat variety of ground beef
upon receiving a higher income, hamburgers are an inferior good, since consumption falls when income
rises. On the other hand, ground beef with a lower fat percentage could be considered a normal good
since consumption is likely to rise when income rises. Normally goods like food in general are said to be
necessities, but since there are different classes of meat on a cow BeefBrazz can differentiate its prices in
the Chilean market according to the various qualities of the different cuts of meat.
Question 9:
By separating the Chilean and South African markets with different demand functions, BeefBrazz is
undertaking third-degree price discrimination, which will maximize profits by exploiting that different
buyers are willing to pay different prices for the same products by separating geographical markets.
In a perfectly competitive market, the firm cannot price discriminate as the firms are price-takers
A monopolist, however, has market power to choose the profit-maximizing price of his product. Since the
demand curves for the two markets BeefBrazz wishes to operate in are different, it is recommendable and
in theory possible to differentiate prices in order to maximize profits.
Question 10:
Given: Joint cost:
MC = 0,07 *Q + 7
CPR-no: 14th January 2013 Managerial Economics Mid-term
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South Africa:
QMAX
P = -0.1 *Q + 40
400
MR = -0.2 *Q + 40
200
Chile:
P = -0.05 *Q + 30
600
MR = -0.1 *Q + 30
300
First we find the quantity for MRSA at the MR-value where Chile enters the scenario.
MR = 30 = -0.2 *Q + 40
Q = 50
The we perform a horizontal addition of the 2 MR's:
MR QDK QS Q Total
40 -
-
-
30 50
-
50
- 200
300
500
The we can find the 2 MR's for the intervals of a=y2-y1/x2-x1 and b=y1-a*x1
MR = -0.200 *Q +
40.00 0 <Q <
50
MR =
-0.066667 *Q +
33.33
50 <Q <
500
We can now draw it: Q MR MC Optimum Optimum
0 40.000 7
30.00
50 30.000 10.5
30.00
50 30.00 10.5
30.00
50 30.00 10.5 0
30.00
50 30.00 10.5
30.00
30.00
500 42
CPR-no: 14th January 2013 Managerial Economics Mid-term
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-
We clearly see that the interception between MR and MC is in the second interval above Q =
50
MR = MC
-0.066667 *Q + 33.33 = 0,07 *Q + 7
Qtotal = 192.68
MRTotal =
20.49 (the MR-value in optimum)
MR optimum is the inserted into the 2 markets MR-functions:
MRSA =
20.49 = -0.2 *Q + 40
QSA =
98
PSA =
30.24
MRC =
20.49 = -0.1 *Q + 30
QC =
95
-
5,00
10,00
15,00
20,00
25,00
30,00
35,00
40,00
45,00
0 100 200 300 400 500 600
MR
MC
CPR-no: 14th January 2013 Managerial Economics Mid-term
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PC =
25.24
TC function: 0.035 Q^2+ 7 Q
Total Revenue, I (PSA*QSA):
2,950.60 Total Revenue (PC*QC), II:
2,401.21
Total Revenue, total (TRSA+TRC):
5351.8139 Total Cost (TC*Qtotal), Total:
2,648
Profit (TRtotal-TCtotal):
2,704
Question 11:
At 0<Q<300 MC is 2 Real pr. kg
At Q = 300 we get an accumulated discount of 5% which gives us a MC at that
output equal to -28 because 2-(300*2*0,05%) = -28
At 301<Q<500 the MC is equal to 2*0,95% = 1,9 Real with the 5% discount
Q MC
1 2
299 2
300 -28
301 1.9
499 1.9
500 1.71
700 1.71
CPR-no: 14th January 2013 Managerial Economics Mid-term
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At Q = 500 we get a non-accumulated discount of 10% meaning that the marginal cost will simply fall to
1.71 Brazilian Real pr. Kg. onwards since 1,9*0,9% = 1,71 Real
MC & AVC
CPR-no: 14th January 2013 Managerial Economics Mid-term
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Question 12:
The relationship depicted above is the typical form of an isoquant which is input combinations that give
the same output (in this case 500). Isoquants have negative slopes in the relevant area due to the more-is-
better assumption. The known values have simply been plotted into an x-y diagram in the above graph.
MRTS is the ratio of the marginal products of the inputs (L and K) in which ratio, they can substitute each
other. MRTS = -K/L = MPL/MPK
Question 13:
The optimality condition for two variable inputs is found at the point of tangency between the isocost line
(TC = L*w+K*r) and the isoquant. This is found at the place where the two slopes are equal to each other
by setting MRTS = wage/rent
MRTS can be calculated with the formula MRTS = -K/L which has been done below for the given
amounts of labour and capital.
We know that the cost of labor (wage) = 400 Real, and the cost of capital (rent) = 50 Real. The price ratio
of the isocost is therefore = 400/50= 8
Q Labor Capital MRTS
500 1 110 500 2 75 35
500 3 58 17
500 4 48 10
500 5 42 6
500 6 36 6
0
20
40
60
80
100
120
0 2 4 6 8 10 12 14
Relationship between Capital (y-axis) and Labor (x-axis)
CPR-no: 14th January 2013 Managerial Economics Mid-term
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500 7 32 4
500 8 29 3
500 9 27 2
500 10 26 1
500 11 25 1
500 12 25 0
As we can observe from the graph above, there is no MRTS value that equals 8 exactly, therefore, we can
conclude that the optimal use of labor and capital lies somewhere in between K = 48 and K = 42 and
between L = 4 and L = 5.To minimize costs, BeefBrazz should therefore hire 4 workers and use 48 units of
capital which gives them a Total Cost = 4*400+48*50 = 4000 at Q=500, assuming that units of labor are
not divisible, since hiring 5 workers and using 42 units of capital would give them a total cost of 4100
(which is more).
Question 14:
A 10% decrease in the price of capital gives us: 50*0,9 = 45 Real. The new slope of the isocost function can
now be given as 400/45 = 80/9 ~ 8,8889
If labor were continuously divisible it is likely that BeefBrazz would substitute away from labor and utilize
more capital due to the lower price of capital. However, since we assumed above that labor is not
continuously divisible the cost-minimizing input of capital and labor will continue to be L = 4 and K = 48
however with a lower Total Cost = 4*400+48*45 = 3760 to produce an output level equal to Q = 500
CPR-no: 14th January 2013 Managerial Economics Mid-term
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Question 15:
Since BeefBrazz’ production equipment is improved, and assuming that this leads to a more efficient
production and that capital/wage costs do not change, BeefBrazz’ is experiencing process innovation. The
isoquants will move/shift towards the origin since it is now possible to produce a higher amount of output
with the same costs. The consequences for BeefBrazz of using this new equipment, assuming that costs
are still the same, means that they are able to produce the same output with a lower Total Cost, meaning
that this would improve their profits, under the assumption that they are the only supplier in the market.
This new situation is illustrated below:
CPR-no: 14th January 2013 Managerial Economics Mid-term
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Question 16:
Since BeefBrazz is cattle-farming firm, it is likely that there is a high degree of attention regarding animal
welfare from the public. It is therefore likely that BeefBrazz should focus on proper treatment of the cattle
and exert a high-degree of respect to animal welfare. Furthermore, cattle-breeding is known to have
somewhat severe impact on the environment due to the vast amounts of resources used to breed cattle.
In this respect BeefBrazz would do well in making sure that their production processes are efficient in such
a way that they strain the environment as little as realistically possible. Other focus areas related to ethical
business conduct could include: respect of human rights, child labour, fair pricing of products, working
conditions and so on.