How does a production possibilities curve illustrate how efficient an economy is?

By itself, a ppc does'nt illustrate efficiency. In a two-good world (which is how PPCs are typically drawn), the PPC represents the maximum production of the two goods, and assumes that inputs are used efficiently. To illustrate efficiency, you need more information.

A production possibilities curve (PPC), also known as a production possibilities frontier (PPF), is a graphical representation of the different combinations of two goods or services that an economy can produce, given its available resources and technology. It shows the maximum potential output for an economy.

The efficiency of an economy can be evaluated by analyzing the position of its PPC. Here's how you can determine efficiency using a PPC:

1. Understand the concept of opportunity cost: The PPC shows the trade-offs an economy faces. To increase production of one good, the economy must decrease production of the other. This concept is known as opportunity cost.

2. Analyze points on the PPC: Points on the PPC represent efficient production combinations, where resources are allocated fully and used optimally. Any point on the PPC indicates that the economy is using its resources efficiently and producing at its maximum capacity.

3. Evaluate points inside the PPC: Points inside the PPC represent inefficient production combinations. These points indicate that the economy is not utilizing all its available resources fully. In such cases, resources are underutilized, leading to a lower level of output.

4. Consider points outside the PPC: Points outside the PPC represent unattainable production combinations. These combinations exceed the economy's current resources and technology. They represent an unachievable level of output.

By analyzing the position of the PPC and identifying whether the economy is on, inside, or outside the curve, you can assess its efficiency. An economy that operates on the PPC is considered efficient, while an economy operating inside the PPC is considered inefficient, and an economy outside the PPC is unattainable.