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process of a perfectly competitive market

The market for beet sugar is purely competitive and entry is free. There are 1000 producers in the industry each of which has a total cost function given by:

TC= 240q - 20q² +q³

The demand: Q= 21,280 - 2P

1- determine the industry's supply curve and graph it.

Suppose the normal production process for beet sugar uses high-sulfur oil for fuel and releases 2 units of sulfur dioxide to the air for every ton of beet sugar produced.
2- then the market reaches short-run equilibrium, how many units of sulfur dioxide does the industry dump into the air per week? Show calculations.
3- An anti-pollution law is passed which requires the industry to burn only low-sulfur oil. The use of low-sulfur oil has the effect of adding $225 to the cost of every ton of beet sugar produced. Otherwise, every productive operation is unchanged. How will this regulation affect the industry supply curve? Draw the new supply curve.
4- When the market reaches (short-run) equilibrium with the regulation in force, how much pollution will the industry produce each week, given that use of low-sulfur oil reduces pollution to 0.75 units of sulfur dioxide per unit of output? Show calculations.
5- What is the effect of the regulation on the price paid by the buyer of beet sugar?
6- Without regulation, how much profits would each firm be making?
7- If there is free entry, what would be the long-run industry price and quantity and what would be the number of firms in the industry (without regulation)?
8- Describe the process in 7 above that would drive the industry into long-run equilibrium.

Solution Preview

The market for beet sugar is purely competitive and entry is free. There are 1000 producers in the industry each of which has a total cost function given by:
TC= 240q - 20q² +q³
The demand: Q= 21,280 - 2P

1- determine the industry's supply curve and graph it.
We know that the supply curve is actually the upward sloping part of Marginal cost curve.
From the total cost function:
MC = dTC / dq = 240 - 40q + 3q²
So the individual supply curve is
P = 240 - 40q + 3q²

Let Q= the industry's quantity supplied, then Q = 1000q as there are 1000 identical producers.
Then we have q = Q/1000, and substitute into the supply function:
P = 240 - 40q + 3q²
P = 240 - 40(Q/1000) + 3(Q/1000)²
P = 240 - 0.04 Q + 3Q²/1000²

Suppose the normal production process for beet sugar uses high-sulfur oil for fuel and releases 2 units of sulfur dioxide to the air for every ton of beet sugar produced.
2- then the market reaches short-run equilibrium, how many units of sulfur dioxide does the industry dump into the air per week? Show calculations.

At ...

Solution Summary

What is the effect of the regulation on the price paid by the buyer of beet sugar?

$2.19