# Essay on Economics

730 WordsMay 4, 20133 Pages
Ep = - 0.36, P = 4 -0.36 = 4/(4-a) -0.36 (4-a) = 4 0.36a = 5.4 a = 5.4/0.36 = 15 Consider the following production functions: ? Y = 10K1/2L1/2 ? Y = 2K + 3L a. Fixing labor employment (L) at 16 units, what is the marginal product of capital when capital employment is 25, 35, and 45 for each production function? Do these production functions exhibit diminishing returns to capital employment? Explain. b. Are labor and capital complements under these production functions? Explain. c. Do these production functions have the property of constant returns to scale? Explain. d. Is either production function a “Cobb-Douglas” function? Explain.  n economics, the Cobb–Douglas functional form of production functions is widely used to represent…show more content…
There is now doubt over whether constancy over time exists. History Paul Douglas explained that his first formulation of the Cobb–Douglas production function was developed in 1927; when seeking a functional form to relate estimates he had calculated for workers and capital, he spoke with mathematician and colleague Charles Cobb, who suggested a function of the form Y = bL^kC^{1-k}, previously used by Knut Wicksell. Estimating this using least squares, he obtained a result for the marginal productivity of capital k to 0.75—which was subsequently confirmed by the National Bureau of Economic Research to be 0.741. Later work in the 1940s prompted them to allow for the exponents on C and L to vary, resulting in estimates that subsequently proved to be very close to improved measure of productivity developed at that time.[1] A major criticism at the time was that estimates of the production function, although seemingly accurate, were based on such sparse data that it was hard to give them much credibility. Douglas remarked "I must admit I was discouraged by this criticism and thought of giving up the effort, but there was something which told me I should hold on."[1] The breakthrough came in using US census data, which was cross-sectional and