The following production function has been estimated for wheat: W = 4 F0.5 L0.25 where, W = Wheat yield (kg/ha), F = Fertiliser (kg/ha) and L = Labour (hours/ha) a) Derive the expression for the least-cost expansion path given that fertilizers cost R12 per kg and labour cost R6 per hour b) If the wheat producer has a budget of R9 000 to spend on fertiliser and labour, how much of each input should he use and what is the quantity of wheat he will produce? c) Derive expressions for the value of marginal product (VMP) of fertiliser and labour given that wheat sells at R72 per kg.
The following production function has been estimated for wheat: W = 4 F0.5 L0.25 where, W = Wheat yield (kg/ha), F = Fertiliser (kg/ha) and L = Labour (hours/ha) a) Derive the expression for the least-cost expansion path given that fertilizers cost R12 per kg and labour cost R6 per hour b) If the wheat producer has a budget of R9 000 to spend on fertiliser and labour, how much of each input should he use and what is the quantity of wheat he will produce? c) Derive expressions for the value of marginal product (VMP) of fertiliser and labour given that wheat sells at R72 per kg.
Chapter9: Production Functions
Section: Chapter Questions
Problem 9.7P
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The following production function has been estimated for wheat:
W = 4 F0.5 L0.25
where, W = Wheat yield (kg/ha), F = Fertiliser (kg/ha) and L = Labour (hours/ha)
a) Derive the expression for the least-cost expansion path given that fertilizers cost R12 per kg and labour cost R6 per hour
b) If the wheat producer has a budget of R9 000 to spend on fertiliser and labour, how much of each input should he use and what is the quantity of wheat he will produce?
c) Derive expressions for the value of marginal product (VMP) of fertiliser and labour given that wheat sells at R72 per kg.
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