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.© BrainMass Inc. brainmass.com October 24, 2018, 7:00 pm ad1c9bdddf
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 ...
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.
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
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?
d. Vintage Cellars sells the units for $9,000 each. This price does not vary with the number of units sold. How many units should Vintage manufacture and sell each month?
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Quantity (Cases) Marginal Cost
a. Given the preceding data, construct a table that reports total cost and average cost at various output levels from 1 to 10 cases.
b. At what quantity is average cost minimized?
c. Does marginal cost always intersect average cost at minimum average cost? Why?
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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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a. Based on historical operations, K alone incurred fixed expenses of $40,000, and L alone incurred fixed expenses of $20,000. Find the break-even point in sales dollars and units for each product separately.
b. Give reasons why the fixed costs for the two products combined are expected to be less than the sum of the fixed costs of each product line operating as a separate business.
c. Assuming that for each unit of K sold, one unit of L is sold, find the break-even point in sales dollars and units for each product.
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With gasoline prices at $3.00 per gallon, consumers are flocking to purchase hybrid vehicles (combination of gasoline and electric motors) that get 50 miles per gallon of gasoline. The monthly payment on a 3-year lease of a hybrid is $499 compared to $399 per month on a conventional, equivalent traditional gasoline car that gets 25 miles per gallon. Both vehicles require a one-time $1,500 payment for taxes, license, and dealer charges. Both vehicles have identical lease terms for the residual value, maximum number of miles allowed without penalty, and so forth.
a. Calculate how many miles the consumer must drive per year to make the hybrid the economical choice over the conventional gasoline-only vehicle.
b. How does your answer to part (a) change if the price of the gasoline is $4.00 per gallon?