Quoting further, “Now, the $47-billion agriculture industry is trying to bring t
ID: 1165482 • Letter: Q
Question
Quoting further, “Now, the $47-billion agriculture industry is trying to bring technological innovation up to warp speed before it runs out of low-wage immigrant workers. California will have to remake its fields like it did its factories, with more machines.
(a) Consider a farmer choosing between workers and machines in the production process. What is thefarmer’s optimization problem? Write it out and explain it.
(b) Demonstrate and explain the farmer’s solution to this problem.
(c) What is the optimality condition? Explain.
(d) Demonstrate and explain why farmers have responded to the increase in wages by hiring less workers and more machines.
(e) Is this the only possible response to a wage increase? If not, demonstrate and explain why not.
(f) What does the difference between your answers to (d) and (e) depend on? How does this explain the difference in behavior? Explain.
Explanation / Answer
a ) Max f(k,l) sub to C = wl+rk
where f(k,l) is production function
l= labour, k = capital
w= wage rate, r = rental rate
Farmer will maximize its ouput subject to its cost function.
b) Farmer will try to maximize its output by reducing its cost . This will give him least cost solution which will be optimal to him.
c) MRTS = w/r , MPL/ MPK = w/r
MRTS = Marginal rate of technical substitution
MPL = Maginal Product of labour
MPK = Marginal Product of capital
d) Farmer will respond to increased wage rate by employing more capital and less labour. Farmer is trying to minimize cost .
b)
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