l Biological pest control has high fixed costs associated with machinery and pre
ID: 1125892 • Letter: L
Question
l
Biological pest control has high fixed costs associated with machinery and predator rearing; farmers experience substantial "learning-by-doing"; and farmers also depend on "network externalities" -- information gained from fellow farmers and extension agents. Finally, if neighboring farmers are spraying pesticides, this will also kill off natural predators. Given these factors, assume we can write an average cost function per ton of output for an individual farmer using biological methods that looks like:
ACb=$100-.01Xb-.1xb + .01Xc
Where: Xb is tons of biological production in the region; Xc is tons of chemical production the region and xb is tons of the farmers production.
1) Fill in the chart below (5 pts).
2) Suppose that chemical intensive farmers have constant average costs equal to $95 per ton, and that prices in this market are driven down to the cost of the lowest cost producer. Define a long run equilibrium as one in which there is no incentive for entry or exit by one more farmer of either type. Consider 5 scenarios listed below and describe which of the following are long run equilibria and of these, which are stable equilibria (10 pts)?
a. 16 biological farmers each producing 50 tons. No chemical farmers.
b. 12 biological farmers each producing 50 tons. 5 chemical farmers each producing 100 tons.
c. 4 biological farmer producing 100 tons. 10 chemical farmers each producing 100 tons.
d. 2 biological farmer producing 100 tons. 10 chemical farmers each producing 100 tons.
e. No biological farmers. 10 chemical farmers each producing 100 tons.
3) Which of these is the most efficient outcome (2 pts)?
In the late 1960’s, after cotton pests developed pesticide resistance, cotton growers in Texas successfully made a shift to biological pest control methods, with government infrastructure support (predator rearing, education) being critical. In Mexico, with no similar support, the cotton industry collapsed. How could this phenomenon be explained using the cost function above (3 pts)?
Explanation / Answer
1)
2) The equlibrium is established at the point where the Long run average cost is minimum in the long run.
a.
ACb = $100 - 0.01Xb - 0.1xb + 0.01Xc = $100 - 0.01(16 x 50) - (0.1 x 50) + (0.01 x 0) = 87
The average cost of chemical intensive farmers is $95.
The long run average cost will be $87. Since all of them are producing at the lowest average cost because of presence of no chemical intensive farmer, this scenario is stable.
b.
ACb = $100 - 0.01Xb - 0.1xb + 0.01Xc = $100 - 0.01(12 x 50) - (0.1 x 50) + 0.01(5 x 100) = 94
The average cost of chemical intensive farmers is $95.
The long rung average cost will be $94. This scenario is not stable because the chemical intensive farmers will exit from the market.
c.
ACb = $100 - 0.01Xb - 0.1xb + 0.01Xc = $100 - 0.01(4 x 100) - (0.1 x 100) + 0.01(10 x 100) = 96
The average cost of chemical intensive farmers is $95.
The long rung average cost will be $95. This scenario is not stable as biological farmers will exit from the market.
d.
ACb = $100 - 0.01Xb - 0.1xb + 0.01Xc = $100 - 0.01(2 x 100) - (0.1 x 100) + 0.01(10 x 100) = 98
The average cost of chemical intensive farmers is $95.
The long rung average cost will be $95. This scenario is not stable as biological farmers will exit from the market.
e.
The long run average cost will be $95, since there are no biological farmers in the market. This scenario is stable since all the farmers are producing at their lowest average costs.
3) Amongst the 5 scenarios that are given, scenario "a" and "e" constitute a balanced equilibrium. While among these two, scenario "a" is the most efficient outcome as farmers here are operating at the lowest average costs, i.e. $87.
ACb Xa Xb Xc a. 19.5 50 800 0 b. 44.5 50 600 500 c. 69 100 400 1000 d. 89 100 200 1000 e. 99 100 100 1000Related Questions
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