How does the law of diminishing marginal returns affect output?

By increasing marginal costs higher than it would have been without the fixed factor being fixed.
The law of diminishing returns or in a broader way, the law of variable proportions, says that with one factor fixed, you to produce increase the output by one unit, the marginal unit, must increase the variable factor in a proportion higher, and to increase the output by the next next unit, you must use even more of the variable factor.
With prices given, the above statement implicitly tells us that the marginal cost of production will be higher than it would be if you could increase the quantity of the fixed factor, because the marginal efficiency of it would increase with more of the variable factor, so it would be better to reduce the amount of variable factor and increase the fixed.
For example, to increase the production in one unit, you must buy 3 units of factor A that is variable, and costs 10 dollars each one, and to increase the output in 2 units you must buy 8 units of factor A, with the same price, but suppose that you could increase the quantity of the fixed factor (that would mean that this factor of production is no longer fixed), you could increase increase the output in 2 with 3 units of A and now with 1 unit of B that costs 30 dollars, the cost would be smaller.
So, with marginal costs with the fixed factor will increase in a higher “velocity” without it the marginal costs would increase slowly. And with a given marginal revenue (expected) with less marginal costs, more output would be sold.

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