How does inflation impact the welfare of the economy? When the government causes inflation through printing money, the individuals who saved their money in the bank are poorer.
Is there a way to determine how different inflation rates impact the welfare of the economy?
I tried answering this question myself using the production function, and, though I was able to come up with some conjectures, I was unable to come to a definite conclusion.
First, there are direct negative effects from inflation, known as the shoe leather cost and menu costs of inflation. These are direct costs which come from price changes: People will carry less cash, need to update their knowledge about prices, firms need to update their prices and wages, and similar. These are usually small, but typically higher given higher inflation rates.

Second, there are direct redistributional effects, which come from the devaluation of money and everything denoted in nominal terms, including most importantly nominal bonds and debt (credits). Usually, we imagine borrowers to be less wealthy than lenders (1). Here (unexpected) inflation will redistribute wealth from the rich to the poor. Under most standard welfare functions, this will be a first-order welfare improvement.

Third, we typically think that poorer people have higher marginal propensity to consume (MPC). Assuming that we are in a situation with inefficiently high savings rates (for example in Keynesian traps), the aforementioned redistribution will improve allocations, but this is typically a second-order effect (but also this will depend on what you believe is true about the Keynesian multipliers).

Wage contracts belong into the second argument, but deserve a special mentioning due to their extensive treatment in the literature.

(1): This is sufficient, but not necessary. In order to get a higher MPC from borrowers than from lenders, it is sufficient that the borrowers are not optimally smoothing consumption over time (for example, because they are up against a borrowing constraint) - we call these types of consumers Hand-to-mouth, because they will typically consume all their disposable income. As long as the distance between the (aggregated) borrowers consumption and what they would like to consume in a frictionless environment is larger than the distance between the (aggregated) lenders' consumption and what they would like to consume in a frictionless environment (2), devaluing debt will increase consumption.

(2): It may sound surprising, but there is a significant mass of wealthy hand-to-mouth consumers. See Kaplan et al, 2014