"The debt-to-GDP ratio is not determined by the government; it is determined by the market demand for debt, which, in turn, depends on the structure of interest rates either determined or influenced by the Federal Reserve."
This is only true for private sector debt. The Fed is a creature controlled entirely by Congress. While federal deficits don't determine what debt level can be sustained in the private sector, they do determine the rate at which that debt can be retired. Debt above the level of deficit spending by Congress must be rolled over as there is no currency available to retire it, or to purchase Treasury debt. If the rate of growth/productivity doesn't match the rate of debt increase the only possible outcomes are default or inflation.
"There is presumably a limit to how much the market is willing or able to absorb in the way of Treasury securities, for a given price level (or inflation rate) and a given structure of interest rates."
Given that federal deficits are the only "funding" source for Treasury debt, it is logical to assume they also set the upper limit of the ability to purchase that debt. One cannot invest or borrow what doesn't yet exist.
"Of course, in reality, a firm that exercises its conversion option is likely to experience share dilution. Similarly, a government that exercises its power to monetize debt is likely to experience a jump in the price level."
There are no similarities between the federal government and any other entity. Congress maintains its monopoly patent on creating the US dollar by Constitutional mandate, meaning it's currency is self funding and its issuance provides the means to service/retire its own debt. The upper limit to such funding without creating inflation is the productive capacity of the overall economy, not a "formula". Price stabilization depends upon growing the potential for productivity, regardless of the number of dollars in circulation.
"Higher interest rates would reduce private sector wealth and increase the cost of borrowing, both of which would serve to reduce private sector spending, slowing economic growth."
Interest paid on the federal debt is simply another way of creating money and injecting it into the private sector. It cannot be a "cost" to the private sector since it becomes someone's asset upon issuance. There is absolutely no necessity for the federal government to "fund" its spending via Treasury debt except as a means of reducing (not increasing) the money supply. Treasury debt is a mutually agreed upon and temporary form of taxation, not a funding mechanism for federal spending, which is self funding.
"It would also serve to increase the government’s carry cost. This, in turn, could result in a set of government austerity measures, which could propel the economy into a deep recession."
This is only true if one assumes there is some gain in a "balanced" federal budget and reduction of the money supply. Such an assumption, if acted upon, would effectively be a theft of the resources and labor the government sector uses without providing a means of retiring net private debt or storing value for that commerce. Adding demand for goods and services without providing the means to pay for them is far more inflationary than simply increasing the money supply.
" All we can say for now is that inflationary pressures appear contained. It would be wise, however, for the government to have a plan in place to deal with this contingency should it arise. The plan might allow for inflation to remain elevated for a period of time as tax-and-spend legislation is recalibrated."
Taking away the ability of millions of people to purchase necessities to avoid the "possibility" of an event that you admit you don't understand is not logical. We might as well charge our elected representatives with keeping us safe from the boogie man in the closet. Federal underfunding of the economy has given us a declining middle class and a bubble/bust economy for close to fifty years now.
How much failure is the American worker willing to tolerate from the self appointed "experts" before s/he realizes that "ANY" misery that can be mitigated with US dollars is entirely a political decision, not sound economics? I would guess that limit is close at hand judging from recent events.
