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1. Graph the production function y = 0.4x + 0.09x^2-0.003x^3 for values of x bet
1. Graph the production function y = 0.4x + 0.09x^2-0.003x^3 for values of x between 0 and 20. Derive and graph the corresponding MPP and APP. What is the algebraic expression for the elasticity of production in this case? Is the elasticity of production constant or variable for this function? Explain.
2. Suppose that the coefficients or parameters of a production function of the polynomial form are to be found. The production function is
y=ax+bx2 +cx3
where y = corn yield in bushels per acre
x = nitrogen application in pounds per acre
a, b and c are coefficients or unknown parameters
The production function should produce a corn yield of 150 bushels per acre when 200 pounds of nitrogen is applied to an acre. This should be the maximum corn yield (MPP = 0). The maximum APP should occur at a nitrogen application rate of 125 pounds per acre. Find the parameters a, b and c for a production function meeting these restrictions. Hint: First find the equation for APP and MPP, and the equations representing maximum APP and zero MPP. Then insert the correct nitrogen application levels in the three equations representing TPP, maximum APP and zero MPP. There are three equations in three unknowns (a, b, and c). Solve this system for a, b, and c.
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