Properties of Production Functions

Production functions in these environments take continuous inputs of each factor, which lets us test an agent's ability to conduct marginal thinking when choosing the composition of inputs. For example, by knowing the hourly wage of hiring an additional worker, the additional output the worker might produce using the particular production process, and the price they can sell the firm's output, they can decide whether hiring the additional worker is profitable. In the absence of prices, this section tests basic decision making of the agent for understanding substitution between factor of production, marginal products for each input, and the understanding of the returns to scale of a production process.

Elements

1. Diminishing Marginal Products

   Describing how the marginal product of an input changes as that input rises with the other input fixed.

2. Marginal Products

   Computing the marginal product of labor or capital for a Cobb-Douglas production function.

3. Output Elasticity

   Computing the elasticity of output with respect to labor for a Cobb-Douglas or linear production function.

4. Returns to Scale

   Classifying a production function as having increasing, constant or decreasing returns to scale.

5. Average Cost

   Deriving a firm's short-run average cost function from its production function, wage and fixed cost.

6. Marginal Cost

   Deriving a firm's short-run marginal cost function from its production function and wage.

7. Elasticity of Substitution

   Computing the elasticity of substitution of a CES technology from its function, from two cost-minimising input ratios, or using it to predict how the input ratio responds to a wage rise.