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ECON1020/ECON1022, Topic 9
发布时间：2023-01-12
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ECON1020/ECON1022, Topic 9
1 Deforestation
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 directly linked to the amount of trees produced. Specifically, it estimated to create a 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, External- ity Cost and Tax Revenue (if relevant) etc. in the usual Supply-Demand picture.
1. 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?
2. 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?
3. Price floor. Suppose that the government decides to introduce a price floor. Assuming that the resulting rationing is resolved in such a way that the most efficient producers sell to the consumers most eager to buy, what should the price floor be to eliminate the dead-weight loss associated with the deforest- ation?
4. Cap-and-trade. Calculate the efficient level of total wood production quota. Describe in words how the government should allocate that quota to the firms. Be explicit which normative criterion you use.
2 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 neighbours. The Marginal Cost of the externality inflicted depends on the firm’s output: MCext = 4 + 2q .
1. What is the utilitarian efficient level of output? What is utilitarian welfare (surplus) then?
2. Assume that the firm has the property rights to the environment and, there- fore, it can legally pollute as much as it pleases. In the absence of an agree- ment with its neighbours, what would its level of output be? Suppose that the neighbours negotiate with the firm. If the negotiations lead to the max- imal 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?
3. 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?
3 Asymmetric information
1. 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 is free. There are 1000 consumers, each with marginal value of the qth 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?
2. 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 competitive equilibrium price, quantity, and welfare?
3. 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?
4. 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?
