**Production Possibility Curve (PPC)**

The production possibility curve (PPC) is a graphical representation that shows the different combinations of two goods that can be produced with the given resources and technology. The PPC is convex when the opportunity cost of producing one good increases as more of it is produced.

**Conditions for Convex PPC**

There are several conditions that must be met in order for the production possibility curve to be convex:

1. **Law of Increasing Opportunity Cost**: The law of increasing opportunity cost states that as more of a good is produced, the opportunity cost of producing an additional unit of that good increases. This means that resources are not perfectly adaptable and are better suited for producing certain goods over others.

2. **Limited Resources**: The PPC assumes that resources are limited and must be allocated between the production of different goods. As a result, producing more of one good means sacrificing the production of another good.

3. **Constant Marginal Rate of Transformation (MRT)**: The MRT is the rate at which one good can be exchanged for another along the PPC. For the PPC to be convex, the MRT must be decreasing. This means that as more of one good is produced, the MRT decreases, indicating that more and more units of the other good must be given up to produce an additional unit of the first good.

**Explanation of Convex PPC**

When the above conditions are met, the PPC will be convex. This means that the curve will be bowed outwards from the origin.

- At the beginning, when the economy is producing a small quantity of one good and a large quantity of the other good, the resources are allocated to their most efficient uses. As a result, the opportunity cost of producing additional units of the first good is relatively low.

- As more units of the first good are produced, resources that are better suited for producing the second good must be reallocated. This results in a higher opportunity cost of producing the first good, as more and more units of the second good must be given up.

- Therefore, the PPC becomes steeper as we move along the curve, indicating the increasing opportunity cost of producing the first good.

- The convex shape of the PPC also reflects the concept of diminishing marginal returns. As more units of a good are produced, the additional output gained from each additional unit decreases.

In conclusion, the production possibility curve is convex when the opportunity cost of producing one good increases as more of it is produced. This is due to the law of increasing opportunity cost, limited resources, and a constant marginal rate of transformation. The convex shape of the PPC illustrates the concept of diminishing marginal returns and the trade-offs involved in allocating resources between different goods.