Purchase Solution

cost function

Not what you're looking for?

Ask Custom Question

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.

Attachments
Purchase this Solution

Solution Summary

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

Solution Preview

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 ...

Purchase this Solution


Free BrainMass Quizzes
Economics, Basic Concepts, Demand-Supply-Equilibrium

The quiz tests the basic concepts of demand, supply, and equilibrium in a free market.

Basics of Economics

Quiz will help you to review some basics of microeconomics and macroeconomics which are often not understood.

Elementary Microeconomics

This quiz reviews the basic concept of supply and demand analysis.

Pricing Strategies

Discussion about various pricing techniques of profit-seeking firms.

Economic Issues and Concepts

This quiz provides a review of the basic microeconomic concepts. Students can test their understanding of major economic issues.