Biological pest control has high fixed costs associated with machinery and preda
ID: 1125903 • Letter: B
Question
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).
ACb xb Xb Xc
a) 50 800 0
b) 50 600 500
c) 100 400 1000
d) 100 200 1000
e) 100 100 1000
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. In long run, the equlibrium point will be at the minimum point of Long run average cost.
a) ACb=$100-.01Xb-.1xb + .01Xc = $100-.01(16*50-.1*50 + .01*0 = 87
and AC for chemical intensive farmers is $95. Hence the long run average cost will be $87. And this is a stavle situation as all of them are producing at the lowest average cost as there is no chemical intensive farmer.
b) ACb=$100-.01Xb-.1xb + .01Xc = $100-.01(12*50)-.1*50 + .01*5*100 = 94
and AC for chemical intensive farmers is $95. Hence the long rung average cost will be $94. This is not a stable situation as chemical intensive farmers will leave the market.
c) ACb=$100-.01Xb-.1xb + .01Xc = $100-.01(4*100)-.1*100 + .01*10*100 = 96
and AC for chemical intensive farmers is $95. Hence the long rung average cost will be $95. This is not a stable situation as biological farmers will leave the market.
d) ACb=$100-.01Xb-.1xb + .01Xc = $100-.01(2*100)-.1*100 + .01*10*100 = 98
and AC for chemical intensive farmers is $95. Hence the long rung average cost will be $95. This is not a stable situation as biological farmers will leave the market.
e) As there is no biological farmers, then long run average cost will be $95. This is a stable situation as all the farmers are producing at the lowest average cost.
3. Among these 5 scenarios "a" and "e" are stable equilibrium. Among these two "a" is the most efficient outcome as it is operating at the lowest average cost, i.e. $87.
Acb Xb 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
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.