Optimizing Fish Catching Crew Size

The assignment content is about a trawler owner who wants to maximize profits by determining the optimal crew size to catch fish. The marginal revenue and cost curves are analyzed, and it is found that the maximum profit occurs when the marginal revenue equals the marginal fixed cost, which happens at a crew size of 9. Additionally, there are four parts to the assignment: (1) finding the optimal crew size for catching fish, (2) analyzing the price-quantity relationship for oil lamps, (3) discussing the market model and competition in the mobile phone industry, and (4) providing advice on how Nokia can compete with Apple and Samsung. The content also includes references to external sources.

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Contents
PART 1.......................................................................................................................................................2
PART 2.......................................................................................................................................................3
PART 3.......................................................................................................................................................6
PART 4.......................................................................................................................................................8
Part 5.........................................................................................................................................................11
References.................................................................................................................................................13
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PART 1
A. Ford is one of the companies who is making profit in automotive industry despite the fact
that it is highly competitive in nature. Some of the reason of existence of profits in Ford
are mentioned and discussed below:
1. Seasonality – Their management tracks down the sale of vehicle when it is manufactured
and delivered to the buyer or the retailer. The scheduling of vehicle production is
dependent on various factors like number of vehicles sold by their dealers or retailers to
the customers and number of vehicles present in the inventory available for sale. Their
manufacturing capacity is higher in first half of the year to meet increasing demand in the
spring and summer which are considered to be the strongest sales month of the year.
2. Procurement of Raw Material – Ford does not rely on one or two raw material
suppliers. They procure wide range of raw materials from many suppliers. To meet
unpredictable demands or tackle any unavoidable circumstances they have made many
sources of raw materials. There is always some risk or uncertainty involved, which can
hamper the availability in sufficient amount to fulfill the company’s requirements.
3. Backlog Orders – To reduce inventory and production loss, the usually manufacture and
ship the units within 20 days after the order is confirmed. It helps in reducing backlog
orders during that period of time.
4. Customer Satisfaction Actions – Customers prefer to buy ford cars because of their
warranty coverage. Their warranties are offered for particular period of time and it varies
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subjected to the type of unit and sales location. They provide free services like repairing,
replacing and adjusting all the parts which are not functioning properly.
B. “The price variation in crude oil impacts the sentiments and hence the volatility in stock
markets all over the world. The world equilibrium price of gasoline fluctuates primarily
because of spikes and collapses in crude oil input prices caused at various times by
supply disruptions and gluts, increasing demand in developing countries, and
speculation.”
When the price of the crude oil fluctuates and it becomes lower, the governments of
various countries increase the excise duties and they increase the VAT too ("Gas Prices
Explained", 2016). This shore up their revenues and the prices of petrol/gasoline are kept
high for the retail consumers. Then, another reason is that when the price of crude oil
fluctuates, the demand for the gasoline starts fluctuating because they are substitutes of
each other (Abhishek Waghmare, 2016). When crude oil becomes expensive, the people
demand gasoline and the higher demand leads to increase in the prices of gasoline. In
Malaysia, the prices of crude oil are fixed using the float system and the prices of petrol
are fixed using the automatic price mechanism. As compared to other countries, the
prices of fuel in Malaysia are static or higher for past few years. Since the price for both
the fuels is determine differently in this country, so the price fluctuations in crude oil has
less impact on the prices of petrol ("Malaysian Petrol Price Compared To Other
Countries - Business Insider", 2014). The other factors that affect the petrol price in
Malaysia are the demand and supply because the prices is fixed automatically with the
interaction of demand and the supply.
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PART 2
Linear Relationship
I Dependent Variable – Quantity
Independent Variables – Price, Income, Advertising
II. Linear relationship between dependent and independent variables can be determined by using
linear regression method. Since the p-value (0.1) of Advertising variable is greater than 0.05, it
means that it is statistically insignificant and hence we will remove this variable. (Refer Sheet –
Linear I)
We will conduct the regression model again without advertising variable to estimate linear
relationship.
The final equation is: Quantity = 179.1476 -10.5313*Price + 1.136883*advertising (Refer
Sheet – Linear II)
III. Chi Square test will be used to determine goodness of fit of estimated demand function. Here
the null hypothesis is Ho = the estimated and actual value are same and Ha = the estimated and
actual value are not same. The formula used to calculate chi square is ∑(observed – expected)^2/
expected. Once the chi square is calculated (which is coming to be 3.7), the p value is calculated
with D.F = 9 and it is coming out to be 0.94. It means we cannot reject the null hypothesis and
hence the model is fitted properly. Also, the adjusted R square value is 0.94 which means 94%
of the variation in dependent variables is correctly estimated by independent variables
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IV. The price coefficient tells us that if the price is increased by one unit then there will be
decrease in quantity demanded by 10.54. The Income coefficient tells us that if the income is
increased by one unit then there will be increase in quantity demanded by 1.14 units. Hence, it
shows that demand is proportionally related with price of the good and income of the consumers.
V. Price elasticity of demand is given by the formula: ∆Q/∆P * P/Q
Here Qo = 160, Q1 = 200, P0 = 5, P1 = 2. Substituting these values in the formula above we get the
price elasticity of demand = -0.417 (the price elasticity of demand is always negative)
Income elasticity of demand is given by the formula: ∆Q/∆I * I/Q
Here Qo = 160, Q1 = 200, I0 = 30, I1 = 35. Substituting these values in the formula above we get
the price elasticity of demand = 1.5(It shows the good is a luxury good)
a. Nonlinear relationship
I. Log (Quantity) = 2.415999669 - -0.384430191*Log (Price) (The Income and Advertising
variables are statistically insignificant in logarithmic form)
II. Yes, the estimated demand function is good. According to chi square test, the p value is
coming out to be 1 which could not reject our null hypothesis which is stated as: The actual and
expected values are same. Also, the R square value is 0.82 which is a good value of fit.
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III. The difference between two models is the elimination of Income variable in the latter model.
In Non Linear relationship the income variable is not significant in explaining the changes in
quantity demanded value. Also, the R square and Adjusted R square value in linear model is
higher when compared with nonlinear due to addition of Income variable in former model.
(Refer Sheet – Non Linear)
PART 3
a. The amount of fish caught per week on a trawler is a function of the crew size assigned to
operate the boat. Based on past data, the following production schedule was developed:
Size Fish Average Marginal
2 3 1.5 0
3 6 2 3
4 11 2.75 5
5 19 3.8 8
6 24 4 5
7 28 4 4
8 31 3.875 3
9 33 3.7 2
10 34 3.4 1
11 34 3.09 0
12 33 2.75 -1
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i. Over what ranges of workers are there
 Increasing returns :- 2-5
 Constant returns 10-11
 Decreasing returns – 5-11
 Negative returns – 11-12
ii. How large a crew should be used if the trawler owner is interested in maximizing the
total amount of fish caught?
Since highest number of fishes caught is when team size is either 10 or 11. To avoid
excess workers, 10 must be the size of crew to maximize the total amount of fishes
caught which are 34. Also at 11 workers, the MP of labor decreases.
iii. How large a crew should be used if the trawler owner is interested in maximizing the
average amount of fish caught per worker?
The average product is highest when 6 or 7 workers are employed. However, 6 workers
are sufficient enough to catch the maximum average amount of fishes. Also at 7 workers,
the MP of labor decreases.
b. Consider the above question again. Suppose the owner of the trawler can sell all the fish
caught for $75 per tonne and can hire as many crew members as desired by paying them
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$150 per week. Assuming that the owner of the trawler is interested in maximizing profits,
determine the optimal crew size.
Size Fish Marginal Total Revenue Marginal
Revenue
2 3 0 225 0
3 6 3 450 225
4 11 5 825 375
5 19 8 1425 600
6 24 5 1800 375
7 28 4 2100 300
8 31 3 2325 225
9 33 2 2475 150
10 34 1 2550 75
11 34 0 2550 0
12 33 -1 2475 -75
At Crew Size of 9, the Marginal Revenue becomes equal to Marginal Fixed Cost (which is 150
for every crew size). Thus, according to the optimal condition, the crew size of 9 will give the
maximum profit.
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PART 4
a. Total Revenue = Price*Quantity
Price = (120000 – Q)/10000
So, TR = 12*Q – Q^2/10000
b. Marginal Revenue = ∂TR wrt Q
MR = 12 – Q/5000
c. Total Cost is equal to Fixed Cost plus Variable Cost
Fixed Cost = 12000
Variable Cost = 1.5Q
TC = 12000 + 1.5Q
d. Marginal Cost = ∂TC wrt Q
MC = 1.5
e. Profit = Total Revenue – Total Cost
= [12Q – Q^2/10000] – [12000 + 1.5Q]
= 10.5Q – 12000 – Q^2/10000
Profit is maximum when Marginal Revenue becomes equal to Marginal Cost so
12 – Q/5000 = 1.5
Q = 52,500
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Since, Price = (120000 – Q)/10000 and Q = 52,500
Price = $6.75
Putting the value of Q in Profit equation we get the value of profit
Profit = 10.5*52,500 – 12000 – 52500^2/10000
Profit = $263,625
f. We know Marginal Revenue = 12 – Q/5000
Putting Q = 52,500 we get MR = 1.5 which is equal to MC
g. What model of market pricing behavior has been assumed in this problem?
Since the price of oil lamp is set at $6.25 which is higher than optimal price ($1.5), the
market model is monopolistic.
10

Part 5
a. During the begining of Iridium, the accessibility of the mobile phones was very por and large
number of people could not use it. The phones were of larger size and they were affordable by
the rich people or the big business houses. There wwas less competition among the firms that
produced the mobile phones and it was just the only medium of communication. There was a
sinlge facuilty that was there in the phone, the voice analog facility.
b. When mobile phones were introduced, they were expensive to buy because the rate of calls
was very high. So, Nokia came up with the mobiles that were cheap and affordable by the
people. It created an intense competition in the market. It came up with the trend of digital
mobile telephony. The other firms in the indutry followed the trend that was started by Nokia of
selling the affordable mobile phones in the market. Also, the company designed web-enabled
phones that could connect to local area networks and eventually the Internet.
c. Motorola would have reduced the price of its mobile phones and it could have offered a
secured ad reliable handset to the customers. Also, the company would have focused on
innovation like Nokia and Apple did if it would have correctly perceived the steps its rival Nokia
would take.
d.Nokia is advised to innovate its products. The software of Apple is unbeatable. So, the Nokia
should tie up with big companies like google for coming up with a new software whoch can
ccompete with ioS. Also, the company many not be able to provide the varioys applications but
it can compete by proviing limited applications but of major use and good qualiity (McCray,
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Gonzalez, & Darling, 2011). The phones of samsung provides number of applications at
affordable prices but the quality and relaibilyt is low. So, Nokia is advised to introduce quality
product at low price. The licensing for the product can also help the company in fighting with the
pressure that the competitors have put on it.
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References
Abhishek Waghmare, I. (2016). Why the 75% Drop in Global Oil Prices Isn’t Reaching You -
The Wire. The Wire. Retrieved 19 October 2016, from http://thewire.in/20964/why-the-75-drop-
in-global-oil-prices-isnt-reaching-you/
Gas Prices Explained. (2016). Gaspricesexplained.com. Retrieved 19 October 2016, from
http://www.gaspricesexplained.com/
Malaysian Petrol Price Compared To Other Countries - Business Insider. (2014). Business
Insider. Retrieved 19 October 2016, from http://www.businessinsider.my/malaysian-petrol-price-
compared-to-other-countries/#66WXQG3lRmtmkUFy.97
McCray, J., Gonzalez, J., & Darling, J. (2011). Crisis management in smart phones: the case of
Nokia vs Apple. European Business Review, 23(3), 240-255.
http://dx.doi.org/10.1108/09555341111130236
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