# Question regarding to Government Debt in Williamson Textbook

I am using the Williamson Macroeconomics textbook to look over a chapter on Monetary Policy and Banking (Chapter 12, 5th Edition).

For a bit of context, the author specifices the government budget constraint as:

$$PG+\left(1+R^{-}\right)B^{-}=PT+B+M-M^{-}$$

wherein it can be understood as a flow budget constraint. The term $PG$ is the amount in dollars of government purchases, and the term $(1+R^{-})B^{-}$ is the payment due on outstanding government debt. The LHS therefore corresponds to government outlays. The RHS consists in nominal terms, government recepits. The first term $PT$ measures nominal taxes, $B$ denotes government bonds, and the final term $M-M^{-}$ deenotes change in nominal money supply.

The question relates to what would happen the nominal money supply increased (the last term $M-M^{-}$ increased).

The explanation on page 455 is as follows: because both sides have to be equal, and one part of the RHS has increased, something has to give way. That means either $PT$ has decreased or $B$ has decreased or both to preserve equality. In the case that $PT$ does not change, the author explains that the government could reduce the quantity of bonds $B$ that it issues during the current period. This is an open market operation wherein the fiscal authority issues debt, and the monetary authority purchases some of this debt by issuing new money. In essence, the author argues that $M-M^{-}$ increases as $B$ decreases. This does not make sense to me, however. If the fiscal authority were to issue more debt, would $B$ not increase? That is, the quantity of bonds in the market would go up in this open market purchase. Am I missing something obvious?

Many thanks!

• You write in your post"This is an open market operation wherein the fiscal authority issues debt, and the monetary authority purchases some of this debt by issuing new money.". Is this you or is this what the author writes in his book in the page you mention? – Alecos Papadopoulos Jan 29 '18 at 21:26
• This is what the author wrote, taken verbatim. – ChinG Jan 29 '18 at 22:41

Given the clarification from the OP in the comments, there appears to be a mix-up here.

We learn that the author explains as follows:

This is an open market operation wherein the fiscal authority issues debt, and the monetary authority purchases some of this debt by issuing new money.

This sentence describes a situation where the monetary authority is separate from government. But if this were so, we could not have in the same budget constraint both inflows from bond issue and from increase of the money supply.

Namely, the budget constraint describes a different situation, one where the government is a single entity that has three options to finance itself:
1) Collect Taxes from the private sector
2) Issue bonds that are purchased by the private sector
3) Issue new money by fiat

In such a case, with fixed outlays in the left-hand side, more money issuance allows indeed for less debt.

I note the the author writes "the monetary authority purchases some of this debt". This complicates things a bit, it means that part of the debt is bought by the private sector, and then we could have a partial substitution effect, but then we would have to distinguish between "debt held by the monetary authority" and "debt held by the private sector", etc.