Why is Walras equilibrium inefficient when we are dealing with public goods? I know that when we have public goods we have that:

$$MRT = MRS_a + MRS_b$$

Though I fail to understand why does this makes Walras equilibrium inefficient.

Thank you very much for your help!
In a competitive market for a private good (y) individuals may consume different quantities but the equilibrium condition requires that: $$ \frac{\frac{\delta u^{i}}{\delta y}}{\frac{\delta u^{i}}{\delta x}} = MRS^{i}_{yx} = MRT_{yx} \; \forall \; i $$

In the case of a public good (g) individuals may have different MRS but consume the same amount of the public good. Then for a given amount of a public good, the marginal benefit is the sum of individual marginal rates of substitution. Therefore, the optimal allocation must satisfy: $$ \sum_{i} \frac{\frac{\delta u^{i}}{\delta g}}{\frac{\delta u^{i}}{\delta x}} = \sum_{i} MRS^{i}_{gx} = MRT_{gx} $$

You can easily see that both conditions are not the same. In the case of an economy with only private goods, the benefit to
society of the last unit of a private good provided (expressed as the
willingness to forgo units of another good) is equal to the benefit of the
one person in society who receives this last unit. If there are some
people who receive a higher benefit from the last unit than others, we
don’t have Pareto efficiency. Hence, the marginal benefit of a private
good must be the same across all people for the allocation to be
efficient. Hindriks and Myles explain this thoroughly if you want to read further on the Samuelson condition versus competitive equilibrium (see Chapter 8 in particular). 

Edit: There is no benefit that producers get here. Think of the MRT as the opportunity cost of producing an extra unit of a good and of the MRS as the marginal benefit of another unit of a good. The marginal cost of a unit of public good is one unit of private good (i.e. the MRT). Therefore the rule says that an efficient allocation is achieved when the total marginal benefit of another unit of the public good, which is the sum of the individual benefits, is equal to the marginal cost of another unit. If the good were private then the marginal benefit of an extra unit can only be attained by a single individual, so there is no sum.