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Within a company is a (micro)economy that is monitored by the accounting procedures. In terms of...

Within a company is a (micro)economy that is monitored by the accounting procedures. In terms of the accounts, the various departments "produce" costs, some of which are internal and some of which are direct costs. This problem shows how an open Leontief model can be used to determine departmental costs. The sales department of an auto dealership charges 10% of its total monthly costs to the service department, and the service department charges 20% of its total monthly costs to the sales department. During a given month, the direct costs are $68,600 for sales and $29,400 for service. Find the total costs (in dollars) of each department. (Round your answers to the nearest whole number.)

sales department $ Incorrect:

service department $ Incorrect: .

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Micro economy
Let cost of Sales department is $ X and cost of Service department is $ Y
So, X= 68,600+ 0.20Y
Y= 29,400+ 0.10X
Substituting the value of X in equation 2:
Y = 29400 + 0.10(68600 + 0.20Y)
Y = 29400 + 6860+.002Y
Y – 0.002Y = 29400+6860
0.98Y = 36,260
Y = 36260/0.98
Y = $ 37,000
So cost of service department is $ 37,000.
Substituting the value of Y in equation 1:
So, X= 68600+ .020Y
So, X= 68600+ 0.20*37000
So, X= 68600+ 7400
X= $ 76,000
So cost of sales department is $ 74,000.
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