Question

I agree and disagree.

As production increases, ones variable costs definitely increase. When production increases even more, one's fixed costs can also increase.

For example, you run a small factory and make tables. It costs Rs.10 for wood for one table. In the small factory you make 1,000 tables per month. Your rent, water, electricity, salaries, etc. (fixed costs) are Rs.6,000 per month. You sell the tables for Rs.30 a table. Assume for this example that all workers are paid fixed wages or salaries, so wages and salaries forms part of fixed costs.

Your income statement currently looks like this:
Sales Rs.30,000
Variable costs (wood) Rs.10,000
Fixed costs Rs.6,000
Profit Rs.14,000

Let's say the demand for your tables increases to 1,100 tables per month. You can still produce this quantity of tables with the current staff and facilities (fixed costs remain the same).

Your income statement now looks like this:
Sales Rs.33,000
Variable costs (wood) 11,000
Fixed costs Rs.6,000
Profit Rs.16,000

Now let's say a short while later the tables start selling really well. Your customers demand 1,500 tables each month. You cannot produce 1,500 in the same factory and with the same number of workers. So you hire more people and move to a bigger factory.

Here's the latest income statement:
Sales Rs.45,000
Variable costs (wood) $15,000
Fixed costs Rs.12,000
Profit Rs.18,000

So, as you can see from this example, your variable costs always change according to production. But when the production increased to a certain point, both your variable and fixed costs would increase. Your fixed costs increase to a new higher level and stay at that level until the next point of expansion.

To give a final answer to your questions above: Yes, fixed costs can vary, but no, when production increases fixed costs would not usually decrease.