Does a catalyst increase the amount of product at equilibrium?

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A catalyst provides an alternative pathway with a lower activation energy. It lowers the energy barrier for the forward reaction and the backward reaction by exactly the same amount, because both directions pass through the same transition state.

So a catalyst speeds up the forward and backward reactions by the same factor, and the equilibrium constant, which is fixed by the ratio of the two rate constants, does not change. Neither does the equilibrium composition. In thermodynamic terms, K is set by ΔG° = −RT ln K, and ΔG° depends only on the reactants and products, which the catalyst does not change.

What does change is how quickly equilibrium is reached. In the Haber process, the iron catalyst does not raise the percentage of ammonia at equilibrium; it lets the plant approach that equilibrium quickly at a temperature where the uncatalysed reaction would be far too slow. Making more product per hour matters enormously in industry, but the equilibrium amount is the same.

Adding a catalyst to a mixture that is already at equilibrium therefore leaves its composition unchanged. The position of equilibrium shifts only when you change concentrations, pressure (for gas reactions with unequal moles of gas on each side) or temperature, and only temperature changes K itself.