To derive a cost function from a production function, you can use the concept of input prices and the production technology. By determining the optimal combination of inputs that minimizes cost for a given level of output, you can derive the cost function. This involves analyzing the relationship between input quantities, input prices, and output levels to find the most cost-effective way to produce goods or services.
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To determine the total cost function for a given scenario, one must identify all the costs associated with the scenario, such as fixed costs and variable costs. By analyzing the relationship between the input factors and the total cost, one can derive a mathematical equation that represents the total cost function. This equation can then be used to calculate the total cost for different levels of input factors in the scenario.
if at-least one factor of production is constant, production function is infact short-run production function
The production function for a firm is the relationship between the quantities of inputs per time period and the maximum output that can be produced. It can be calculated for one or more than one variable factors of production. The one variable factor of production function corresponds to the short-run during which at least one factor of production is fixed .
It has a lower opportunity cost for production of that good.
To derive the Marshallian demand function from a utility function, you can use the concept of marginal utility and the budget constraint. By maximizing utility subject to the budget constraint, you can find the quantities of goods that a consumer will demand at different prices. This process involves taking partial derivatives and solving for the demand functions for each good.