**Introduction**

Average product is a concept used in economics to measure the productivity of labor or capital in the production process. It is calculated by dividing the total product (output) by the quantity of the input factor (labor or capital). The average product represents the average output per unit of input.

**Explanation**

Average product can never become zero or negative in production and cost due to several reasons:

**1. Law of Diminishing Marginal Returns**

The law of diminishing marginal returns states that as more units of a variable input (such as labor) are added to a fixed input (such as capital), the marginal product of the variable input will eventually decrease. This means that at some point, the additional output produced by each additional unit of input will decrease. However, the average product may still be positive as long as the total product is increasing.

**2. Assumptions of Production Function**

The concept of average product assumes certain conditions in the production function, such as fixed proportions of inputs and constant technology. These assumptions imply that the average product will never become zero or negative. If the average product were to become zero or negative, it would violate these assumptions.

**3. Negative Average Product is Infeasible**

A negative average product would imply that the input is actually reducing the total product, which is not feasible in a production process. It would mean that the input is causing more harm than good, resulting in a decrease in output. In reality, firms would not continue to employ an input that has negative average product as it would lead to losses and inefficiency.

**4. Cost Considerations**

From a cost perspective, negative average product would imply that the input is not generating enough output to cover its costs. In competitive markets, firms would not continue to use an input that has negative average product as it would lead to losses. Therefore, negative average product is not economically viable.

**Conclusion**

In summary, average product never becomes zero or negative in production and cost due to the law of diminishing marginal returns, assumptions of the production function, infeasibility of negative average product, and cost considerations. These factors ensure that the average product remains positive, indicating a level of productivity and efficiency in the production process.