Decreasing returns to scale: alpha + beta + gamma If for given values of L,K, and M, the Hessian of the production function f is negative definite, then its isoquants at that point are concave to the origin. Production functions need to have certain properties, to ensure that we can solve the least-cost problem: Check any of the many textbooks. L^ alpha means "raise the value of L to the power of the value of alpha." The symbol "^" means "raise to the power," i.e. Where L = labour, K = capital, M = materials and supplies, and q = product. ![]() The three factor Cobb-Douglas production function is: ![]() If you have not already done so, look at how the parameters of a Cobb-Douglas production function can be estimated: Estimating a Cobb-Douglas production function. A profit maximizing firm will try to use a combination of inputs that will minimize its cost of producing a given level of output. Recall that a production function produces levels of output for combinations of inputs. Now I will show how cost functions look when they are obtained from a production function. In the oligopoly / government enterprise model, I derived each firm's short run cost function from a quadratic, long run, average cost function. ![]() Please show your support by joining Egwald Web Services as a Facebook Fan: Egwald Economics - Production Functions: Cobb-Douglas Production FunctionĮgwald's popular web pages are provided without cost to users.
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