Question

differences between production function and cost function"? long answer Question​

Answer 1

A production function shows the quantity of output we obtain from quantities of inputs. The production functions for some products require one, specific mix of inputs to achieve a target output. For these functions, there is only one recipe for producing the target amount of output (Leontief production functions). Other production functions (Cobb-Douglas (CD), Constant Elasticity of Substitution(CES), etc. production functions) allow different blends of inputs to achieve a target amount of output. These functions allow for substitutions among the inputs.

We derive the cost function from the production function, the prices of the inputs, and the target output. For a Leontief production function, the cost function is simply the sum of the cost of the inputs (quantity of each input times the price of that input) required to product the target output.

For production functions that allow substitution, different blends of inputs, to obtain the target output, the cost function is simply the sum of the cost of inputs for the blend of inputs that is least expensive. For all the blends of inputs that we might use to produce, for example, 100 units of output, the cost function shows us the cost of the blend that produces the 100 units most inexpensively. When the production functions are smooth and the supply curves of inputs are smooth, the cost function is smooth: the lowest cost is a smooth function of the input prices and the target output. In this case, we derive the cost function formally by minimizing the total cost of inputs (sum of the quantity of each input times its price) subject to the constraint that the output of the production function equals the target output.

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