# cost function

I need to define the cost function of a firm given the production function, rent and labor costs. Also about the equation that would minimize costs and the respective ratio.

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Hello!

Question 2

Since there are are 5 (fixed) assembly machines installed at the plant, the production function becomes:

q = 5*5*L

q = 25*L

In order to find the cost function, we must find out how many teams are needed to build a single engine. This is easily done by isolating L from the production function:

L = q/25

Now, the cost function will be:

Cost(q) = 2000*q + 5000*L + 50000

The 2000*q term is the cost of the raw materials. The 5000*L term is what the firm pays in wages ($5000 per team). Finally, the 50000 comes from the fact that there are 5 machines and each machine costs $10000.

Replacing L as a function of q in this equation, as we found earlier, gives:

Cost(q) = 2000*q + 5000*q/25 + 50000

Cost(q) = 2000*q + 200*q + 50000

Cost(q) = 2200*q + 50000

Notice that due to the form of the production function, there are no diminishing returns to labor; so the cost function is linear with respect to q.

Average cost is simply calculated as Cost/q. In this case we get:

Avg Cost = 2200 + 50000/q

Marginal cost is calculated as the first derivative of Cost with respect to q. This gives:

Marginal cost = 2200

As you can see, the marginal cost is constant ...

#### Solution Summary

This job defines the cost function of a firm given the production function, rent and labor costs.

Vintage Cellars: Evaluate Decision-Making Scenarios Using Linear Profit, Cost Modeling

Evaluating Decision-Making Scenarios Using Linear Profit and Cost Modeling

Analyze cost behaviors and decision-making scenarios using linear profit and cost modeling. In a Word document, complete the exercises below and submit your responses per the instructions that follow.

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Vintage Cellars manufactures a 1,000-bottle wine storage system that maintains optimum temperature (55-57 °) and humidity (50-80%) for aging wines. The system has a backup battery for power failures and can store red and white wines at different temperatures. The following table depicts how average cost varies with the number of units manufactured and sold (per month):

Quantity Average Cost

1 $12,000

2 10,000

3 8,600

4 7,700

5 7,100

6 7,100

7 7,350

8 7,850

9 8,600

10 9,600

Required:

a. Prepare a table that computes the total cost and marginal cost for each quantity between 1 and 10 units.

b. What is the relation between average cost and marginal cost?

c. What is the opportunity cost of producing one more unit if the company is currently producing and selling four units?

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Quantity (Cases) Marginal Cost

1 $500

2 400

3 325

4 275

5 325

6 400

7 500

8 625

9 775

10 950

Required:

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Required:

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Line K Line L

Amount Per Unit Amount Per Unit Combined Amount

Sales Revenue $120,000 $1.20 $80,000 $0.80 $200,000

Variable expense 60,000 0.60 60,000 0.60 120,000

Contribution margin 60,000 $0.60 $20,000 $0.20 80,000

Fixed expense 50,000

Net Income $30,000

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Required:

a. Calculate how many miles the consumer must drive per year to make the hybrid the economical choice over the conventional gasoline-only vehicle.

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