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average and marginal costs curves

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To solve this exercise I have to use the results of the exercises solved in the document attached.

Assume that the demand curve has the form of D = 7500/p.
Without congestion the p equals the average costs of road traffic and D is the volume of traffic.

Draw the average and marginal costs curves as well as demand curve into the same graph (you have derived the functions in the previous exercise).

Determine the optimal level of traffic q* visually from the graph and then mathematically check your solution.

What toll should be collected from the road users in order to achieve the optimal use of road capacity?

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Solution Preview

See the attached file.

1. Determine a total cost function of transport services (e.g. road freight) as a function of volume of production. How you can derive now the average cost and the marginal cost of production? Why it is important to know and to be able to formulate average and marginal cost functions when we are interested in evaluating the natural monopoly?

Let Q = volume of production
TC = Total Cost

TC = 300Q + 10000

You can derive the Average cost (AC) by dividing the TC by Quantity.

AC = [300Q + 10000]/Q

You can determine the Marginal Cost (MC) by taking the derivative of TC with respect to Quantity

MC = 300

It is important to know what your average cost is because if the price is below AC, you are losing money. It is important to know the MC if you are a natural monopoly because the profit maximizing quantity is at the point at which MC = MR. Prior to that quantity point, ...

Solution Summary

The solution depicts average and marginal costs curves in this case.