Academic journal article Journal of Money, Credit & Banking

A Simple Model of the Gold Standard

Academic journal article Journal of Money, Credit & Banking

A Simple Model of the Gold Standard

Article excerpt

This paper presents a model of the gold standard in which technology and

preferences are modeled explicitly, and account is taken of both the

durability of gold and the exhaustibility of gold ore. We examine the

steady state and its associated dynamics, and show how the steady-state

price level responds to changes in exogenous factors. Provided we have an

interior solution with unmined gold in the steady state, this price level

rises with technological progress in gold mining, and falls with increases

in real income and the discount rate. However, the steady-state price level

behaves somewhat differently if we have a comer solution.

Despite the enormous literature on the subject, our understanding of the gold standard is still limited. Existing models are inadequate in several respects. For example, many treat the gold supply function or even the gold supply itself as fixed (for example, Barro 1979, Barsky and Summers 1988) and yet, ideally, the supply of gold should be derived from an optimization exercise in which the underlying technology is modeled explicitly. Also, while many models acknowledge the durability of gold (for example, Bordo and Wilson 1985), few provide a satisfactory treatment of the intertemporal implications of gold durability. Nor do most studies take seriously the point that the supply of gold ore is limited and nonrenewable (that is, gold ore is exhaustible). Exhaustibility introduces an additional source of intertemporal interdependence into the model, and its implications have received relatively little attention in the gold standard literature.(1) The durability of gold and the exhaustibility of gold ore mean that we cannot solve for the current-period output of gold, and hence, its current relative price, without solving for the output and price of gold in all future periods as well; they therefore make the analysis considerably more difficult than it would otherwise be.

This paper presents a model of the gold standard that derives the supply of gold from technology and taste parameters, but which also takes account of the durability of gold and the exhaustibility of gold ore. The model is simple, and yields straight-forward expressions for the steady state that enable us to analyze the impact of changes in primitive parameters on the gold standard price level. It also enables us to examine the corner solution as well as the interior one, and to investigate the transition to the steady state as well as the steady state itself.

THE MODEL

A representative agent derives utility services from gold. These services include nonmonetary services, such as the enjoyment of gold as an ornament, but might also include monetary services as well, for example, reduced exchange costs due to the use of gold coins as a medium of exchange). Our model is consequently general enough to encompass both directly convertible gold standards in which there is a positive monetary demand for gold (as medium of exchange), and indirectly convertible gold standards in which the monetary demand for gold is zero.(2) However, gold is the numeraire commodity (that is, nominal prices are quoted in terms of units of gold) in either case. Indeed, it is the fact that gold is numeraire that enables us to interpret our model as one of a gold standard. In short, our treatment emphasizes gold's role as numeraire, but does not preclude gold playing other roles as well.

From a purely formal point of view, we therefore have a model of a single agent who derives (unspecified) services from holding gold. To simplify the exposition, imagine that this agent, Robinson Crusoe, lives on an otherwise uninhabited island. He lives by eating bananas that grow on the island, and bananas grow so abundantly that there is never any danger of his having nothing to eat. The reader who wishes to do so can think of bananas as a proxy for a general nondurable consumption good. …

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