Deriving Factor Demand

This module tests the agent's ability to act in the role of a profit maximizer in non-strategic situations where they take as given the price which they could sell goods they produce, and must pay for inputs to their production process at market rates (e.g., a competitive wage). Whereas in Deriving Demand, the agent was solving a utility maximization problem subject to a budget constraint, here they solve a profit maximization problem constrained by a production function. We test decisions on the quantity and composition of inputs, and the quantity of output for canonical production functions such as Cobb-Douglas and Leontief production functions given the agent's understanding of production functions from Properties of Production Functions. The agent is asked to derive the factor demand functions from first principles from profit maximization and test their ability to reason with the dual cost-minimization formulation—analogous to the Hicksian vs. Marshallian demand of Deriving Demand.

Elements

1. Expenditure Minimization

   Finding the cost-minimising labor, capital or total cost to produce a target output.

2. Profit Maximization

   Finding the short-run profit-maximising labor input, or the resulting profit, for a price-taking firm.

3. Duality of Profit Maximization and Expenditure Minimization

   Recognising that a firm's long-run profit-maximising inputs are also the cheapest way to produce the output they make.