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Introduction to Modern Economic Growth
greater investments. Therefore, in this model Tobin’s q, or alternatively the costate
variable q (t), will play the role of signaling when investment demand is high.
The q-theory of investment is one of the workhorse models of macroeconomics
and finance, since proxies for Tobin’s q can be constructed using stock market prices
and book values of firms. When stock market prices are greater than book values,
this corresponds to periods in which the firm in question has a high Tobin’s q–
meaning that the value of installed capital is greater than its replacement cost,
which appears on the books. Nevertheless, whether this is a good approach in
practice is intensely debated, in part because Tobin’s q does not contain all the
relevant information when there are irreversibilities or fixed costs of investment,
and also perhaps more importantly, what is relevant is the “marginal q,” which
corresponds to the marginal increase in value (as suggested by equation (7.65)),
whereas we can typically only measure “average q”. The discrepancy between these
two concepts can be large.

7.8. Taking Stock
This chapter has reviewed the basic tools of dynamic optimization in continuous
time. By its nature, this has been a technical (and unfortunately somewhat dry)
chapter. The material covered here may have been less familiar than the discrete
time optimization methods presented in the previous chapter. Part of the difficulty
arises from the fact that optimization here is with respect to functions, even when
the horizon is finite (rather than with respect to vectors or infinite sequences as in
the discrete time case). This introduces a range of complications and some technical
difficulties, which are not of great interest in the context of economic applications.
As a result, this chapter has provided an overview of the main results, with an
emphasis on those that are most useful in economic applications, together with
some of the proofs. These proofs are included to provide the readers with a sense
of where the results come from and to enable them to develop a better feel for their
intuition.
While the basic ideas of optimal control may be a little less familiar than those

of discrete time dynamic programming, these methods are used in much of growth
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