The utility function and production function are the same things to different people.

The utility function is concerned with the consumer, whereas the production function is concerned with the producer.

The utility function is a mathematical function that assigns a number to each bundle of goods consumed by a consumer, with higher numbers indicating preferred bundles.

The production function is a mathematical function that shows the relationship between the number of goods produced (output) and the factor of production (inputs) that enable them to be produced.

Differences Between Utility Function And Production Function

1. Utility function shows the relationship between preference levels from consumer purchases whereas the production function shows the relationship between inputs and outputs 

2. Production function is the function of the producer whereas utility function is the function of the consumer

3. The utility function is derived from preferences, whereas the production function is derived from technologies

4. Production function is cardinal because the output produced by each combination of inputs is measurable.

In contrast, the utility function is ordinal as satisfaction is not measurable. The utility function only ranks bundles of goods based on preference.

5. The slope of the production function is marginal product whereas the slope of the utility function is marginal utility.

6. In the production function, isoquants are used to indicate the combination of two inputs that will produce the same level of outputs.

In the utility function, Indifference curves are used to show the combination of two goods that will give the consumers the same level of utility.

Isoquants and indifference curves are two sides of the same coin. Isoquants relate to the producer whereas the indifference curve relates to the consumer. This is the reason why the slope of isoquants is called the marginal rate of technical substitution while the slope of indifference curves is called the marginal rate of substitution.

7. Isocosts is used in a production function to show which input combinations can be used given the firm's budget constraint, whereas the budget line is used in a utility function to show which plausible combinations of two goods can be purchased by a consumer given his budget constraint.

Simply put, the isocost line shows the firm's budget constraint when purchasing factors of production whereas the budget line shows the consumer's budget constraint when purchasing a bundle of two goods.

8. The utility function seeks to maximize utility while the production function seeks to minimize cost.

If you got questions relating to this topic, feel free to ask me in the comment box.

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