Matrices - Economics based question

In summary, the island's economy has three sectors - tourism, transportation, and services - with specific input requirements for each sector's output. The consumption matrix for this economy is shown in part (a). Part (b) asks for the input from the tourism sector required by the services sector, which is $1,000,000. In part (c), the total value of inputs consumed by each sector during production is calculated to be $7,000,000 for tourism, $12,000,000 for transportation, and $5,000,000 for services. The concept of "net production" is not clearly defined, making it difficult to calculate in part (d). Finally, part (e) asks for the gross production
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Homework Statement


An island's economy is divided into three sectors-tourism, transportation, and services. Suppose that each dollars worth of tourism output requires inputs of $0.30 from the tourism sector, $0.10 from the transportation sector, and $0.30 from the services sector; each dollars worth of transportation output requires inputs of $0.20 from the tourism sector, $0.40 from the transportation sector, and $0.20 from the services sector; and each dollars worth of services output requires inputs of $0.05 from the tourism sector, $0.05 from the transportation sector, and $0.15 from the services sector.

(a) Write the consumption matrix for this economy.

(b) If the gross production for this economy is $10 million of tourism, $15 million of trans-
portation, and $20 million of services, how much input from the tourism sector is required
by the services sector?

(c) If the gross production for this economy is $10 million of tourism, $15 million of trans-
portation, and $20 million of services, what is the total value of the inputs consumed by
each sector during the production process?

(d) If the total outputs of the tourism, transportation, and services sectors are $70 million, $50million, and $60 million, respectively, what is the net production of each sector?

(e) What gross production is required to satisfy exactly a demand for $30 million of tourism, $50 million of transportation, and $40 million of services?

The Attempt at a Solution


I'm stuck on part d), but I'll show you my answers and working for previous parts anyway...

a)
http://img174.imageshack.us/img174/9486/18752815lh9.jpg [Broken]

b) $1,000,000 worth of input is required by the services sector from the tourism sector

c) total value of inputs consumed by the tourism sector is $7,000,000
total value of inputs consumed by the transport sector is $12,000,000
total value of inputs consumed by the services sector is $5,000,000

d) I don't understand how one calculates "net production".
 
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The total outputs of each sector are already given, so I'm not sure what is being asked here. Could you please clarify the question?

e) This question is asking for the opposite of part c). Instead of finding the total value of inputs, we need to find the total value of outputs. So, the gross production for the tourism sector would be $30 million, for the transportation sector would be $50 million, and for the services sector would be $40 million.
 

1. What are matrices used for in economics?

Matrices are used in economics to represent and analyze economic data, such as market trends, production outputs, and input-output relationships. They can also be used to solve systems of equations and optimize economic models.

2. How are matrices applied in game theory?

In game theory, matrices are used to represent the payoffs for different strategies in a game. This allows economists to analyze and predict the outcomes of different strategies and make decisions based on the potential payoffs.

3. Can matrices be used to analyze supply and demand?

Yes, matrices can be used to analyze supply and demand by representing the quantities of goods and services supplied and demanded at different prices. This can help economists understand market equilibrium and make predictions about changes in supply and demand.

4. How are matrices used in input-output analysis?

In input-output analysis, matrices are used to represent the interdependent relationships between different industries in an economy. This allows economists to study the effects of changes in one industry on others and analyze the overall economic impact.

5. Do all economists use matrices in their work?

While not all economists use matrices in their work, they are a commonly used tool in economic analysis and modeling. Many economic theories and models rely on matrices to represent and solve complex systems and make predictions about economic behavior.

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