suppose that a producer of commodity Y is located on the upstream of river Z. the MC of producing Y is given by the function of MC= 10 – 0.5Y. in addition this MC however an external cost is incurred. each unit of product Y produces a pollutant that flows the river, which causes damage valued at birr 10. suppose that this external cost borne by the wider community rather than the polluted firm. MR obtained from each unit of Y is given by MR= 30-0.5y a) drive the profit maximizing level of output for Y. b) drive the socially optimum level of output for Y. c)explain why the socially efficient level of output lower than the profit maximum level of output of Y

Answer:

Profit Maximizing Level of Output for Commodity Y

A producer of commodity Y located on the upstream of river Z has a marginal cost (MC) of producing Y given by the function of MC= 10 – 0.5Y. In addition, an external cost is incurred. Each unit of product Y produces a pollutant that flows the river, which causes damage valued at birr 10. The marginal revenue (MR) obtained from each unit of Y is given by MR= 30-0.5y.

Profit Maximizing Level of Output

The profit maximizing level of output for Y can be obtained by setting the MC and MR equal to each other. This means that MC=MR=10-0.5Y. Solving for Y gives the profit maximizing level of output for Y as 20 units.

Socially Optimal Level of Output

The socially optimal level of output for Y can be obtained by taking into account the external cost of producing Y. The external cost of producing Y is the damage to the river caused by the pollutant, which is valued at birr 10. In order to determine the socially optimal level of output, the external cost must be added to the MC. This gives us a new MC of 20-0.5Y. Setting this MC equal to MR gives us the socially optimal level of output for Y as 10 units.

Difference Between Profit and Social Optimal Level of Output

The difference between the profit maximizing level of output and the socially optimal level of output is due to the external cost of producing Y. The external cost of producing Y is the damage to the river caused by the pollutant, which is not taken into account in the profit maximizing level of output. This means that the external cost of producing Y is not considered when the profit maximizing level of output is derived. However, when the socially optimal level of output is derived, the external cost of producing Y is taken into account, resulting in the socially optimal level of output being lower than the profit maximizing level of output.

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