Suppose that a cattle rancher and a wheat farmer operate in to adjoining plots of land. The cattle accationally stray into the wheat field and damage some of the wheat. 4
Cattle rancher has a marginal cost function MPC B = 5Q B (B for beef), and a constant marginal benefit of MSB B = 50. Wheat farmer has a marginal cost function MPC W = Q W , and a constant marginal benefit of MSB W = 20. The negative externality in the problem can be express by the MEC = 10. (1) Efficient allocation Output of beef should be at the level where MSB B = MSC B = MPC B + MEC 50 = 5Q B + 10, Q B * = 8. Output of wheat should be at the level where MSB W = MSC W Q W * = 20. Now let’s see how the clarification of property rights can achieve efficiency if bargaining is costless. (2) Cattle rancher is granted the property rights If rancher has the property rights, he is free to choose any output level of beef. Let’s start at the profit maximizing level of beef, where the MPC is equal to the MSB. 50 = 5Q B . Q B = 10. But some gains from trade are unrealized at this output level. We can use the graphs which are similar to those on page 94 to show that the rancher will accept a payment from the wheat farmer to reduce the size of the herd to Q B * = 8. Q: What is the maximum amount the wheat farmer is willing to pay to reduce the herd size to 8? Q: What is the minimum amount the rancher is willing to accept in order to make such deal?
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