To give some structure, I will follow some definitions in Mas-Colell, Whinston, and Green:

• Let $\mathbf{x}_i$ as the consumption vector of individual $i$.
• Let $\mathbf{y}_j$ be the production vector of firm $j$.

Define an allocation in an economy as a specification of the consumption vector for each individual and the production vector for each firm.

$$ \left(\mathbf{x}, \mathbf{y} \right) = \left(\mathbf{x}_1, \mathbf{x}_2, \ldots, \mathbf{x}_n, \mathbf{y}_1 \ldots \mathbf{y}_m \right) $$

An allocation is feasible if the consumption bundle can be produced from the production technology and the initial endowment $\mathbf{e}$. $$ \sum_i \mathbf{x}_i = \mathbf{e} + \sum_j \mathbf{y}_j \quad \quad \mathbf{y}_j \in Y_j $$

Where $\mathbf{y}_j \in Y_j$ means that the production decision $y_j$ is in the set of production possibilities $Y_j$. If you don't follow the math, that's fine. The basic idea is that an allocation is a complete description of what each individual consumes and what each firm produces.

The economic calculation problem:

How does an economic system choose an allocation from the feasible set? How does one figure out what each individual should consume and each firm should produce?

The classic definition of an economic problem is one where limited means may be put towards alternative ends.

• Making the fastest car possible with a given set of inputs is an engineering problem.
• Making the best possible car, where there are tradeoffs between speed and safety is an economic problem.
• Whether to use parts to build a fast car or a delivery truck is an economic problem.

I would call anytime you solve an economic problem as "economic calculation," but I don't know for sure exactly how your instructor is using/defining it.

Classic, economy wide economy wide calculation question:

To give some structure, I will follow some definitions in Mas-Colell, Whinston, and Green:

• Let $\mathbf{x}_i$ as the consumption vector of individual $i$.
• Let $\mathbf{y}_j$ be the production vector of firm $j$.

Define an allocation in an economy as a specification of the consumption vector for each individual and the production vector for each firm.

$$ \left(\mathbf{x}, \mathbf{y} \right) = \left(\mathbf{x}_1, \mathbf{x}_2, \ldots, \mathbf{x}_n, \mathbf{y}_1 \ldots \mathbf{y}_m \right) $$

An allocation is feasible if the consumption bundle can be produced from the production technology and the initial endowment $\mathbf{e}$. $$ \sum_i \mathbf{x}_i = \mathbf{e} + \sum_j \mathbf{y}_j \quad \quad \mathbf{y}_j \in Y_j $$

Where $\mathbf{y}_j \in Y_j$ means that the production decision $y_j$ is in the set of production possibilities $Y_j$. If you don't follow the math, that's fine. The basic idea is that an allocation is a complete description of what each individual consumes and what each firm produces.

The economic calculation problem in this context is how does an economic system choose an allocation from the feasible set? How does one figure out what each individual should consume and each firm should produce?