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ECON1022 :Assume that the firm has the property rights to the environment and, therefore, it can legally pollute as much as it pleases: Principles of Microeconomics Assignment, UOS, UK
|University of Southampton (UOS)
|ECON1022: Principles of Microeconomics
All questions below are based on the following scenario. Suppose that the inverse demand curve for wood is p = 200 − Q, and the private marginal cost of the firms (that is, the unregulated supply function) is MCP = 80+Q. As it happens, cutting down trees generates all kinds of harmful effects not covered by unregulated loggers. For instance, floods occur more often, and soil erosion proceeds much faster. This externality is estimated to create marginal harm of MCE = Q, so that the true total social marginal cost is MCS = MCP + MCE = 80 + 2Q.
You may illustrate the related Consumer Surplus, Producer Surplus, Externality Cost and Tax Revenue (if relevant) etc. in the usual Supply-Demand picture.
- Unregulated market. Find a competitive equilibrium (pe
, Qe) if this market is left unregulated. What is the dead-weight loss relative to the welfare-maximizing social outcome?
- Pigouvian tax. Suppose that the government imposes a tax of t per unit of
wood to reduce the damage caused by this deforestation. What should t be
to eliminate the dead-weight loss?
- Pollution—Coasian approach
A firm’s private Marginal Cost is MC (q) = 8q, where q is the level of output. It can sell any number of units of output at the world price of 64. However, production inflicts damage on the firm’s neighbors. The Marginal Cost of externality inflicted depends on the firm’s output: MCext = 4 + 2q
- What is the utilitarian efficient level of output? What is utilitarian welfare?
- Assume that the firm has the property rights to the environment and, therefore, it can legally pollute as much as it pleases. In the absence of an agreement with its neighbours, what would its level of output be? Suppose that the neighbours negotiate with the firm. If the negotiations lead to the maximal utilitarian welfare, what is the minimum payment that the neighbours
must make to the firm to achieve the associated change in output? What is
the maximum payment?
- Assume that the neighbours have the property rights, so they can impose
legal punitive damages if the firm pollutes at all. In the absence of an
agreement between the firm and its neighbours, what would the level of
output be? If an agreement maximizing utilitarian welfare between the firm
and its neighbours is negotiated, what are the smallest and largest payments
that the firm would have to pay?
- Assume that the firm has property rights. If the government wishes to
control the externality by imposing Pigouvian tax in the form of a unit tax
on firms, what should the tax be to maximize utilitarian efficiency? How
much revenue does it collect?
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- Asymmetric information
- Suppose a conventional competitive market for a high-quality product. There
are many firms, each with no fixed cost and a marginal cost of MCH = 10 per
unit. Entry and exit are free. There are 1000 consumers, each with a marginal
value of the unit is MVH = 30 − q. In other words, their individual demand curve is q = 30 − p. What are the market demand and market supply curves? What is the equilibrium price, quantity, and welfare?
- Consider an alternative scenario. Suppose that the product on this market is of low quality. A low-quality product is cheaper to produce, the marginal cost is MCL = 6 per unit. Entry and exit is free. But the marginal value from a low-quality product is also lower, MVL = 20−q. In other words, their individual demand curve is q = 20 − p. What are the market demand and market supply curves? What is the equilibrium price, quantity, and welfare?
- Suppose that both high and low-quality firms can exist at the same time
and offer their products. The costs of production of both products are the
same as above, and there are no barriers to entry or exit. Each consumer
can inspect the product and identify its quality. Each consumer has to decide
whether to buy a high or low-quality product at the quality-dependent market
price. Assume that consumers cannot mix the qualities, they have to pick
one. After they decide, their marginal values depending on the quality are
the same as above. What is the equilibrium price for each quality? Which
quality would the consumers choose? What are the equilibrium quantities
in each market?
- Suppose the situation is like in point 3, but no consumer can tell the qualities
apart (Firms know whether they are producing and selling a high quality or a low-quality product). Obviously, if both qualities are traded in equilibrium, they must be traded at the same price. What is the equilibrium price and quantity? What do consumers believe about the quality of the product in equilibrium?1 What are the welfare effects of asymmetric information?
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