# A Quick Overview of the “q Theory” of Investment

Tobin’s q is defined as the ratio of market value to replacement value for a firm’s capital.

The market value in the numerator reflects the profitability to the firm of one additional unit of capital.  The replacement cost in the denominator can be thought of either as the cost of acquiring new capital or the price earned by selling existing capital.

If q>1, then the additional profit a firm could expect from one more unit of capital (equipment, buildings, etc) is greater than its replacement/acquisition cost.  The firm should increase its capital stock.

If q<1, then the additional profit would be less than the acquisition cost.  We assume diminishing marginal productivity of capital, so this also means that the last unit of capital the firm acquired is producing less for the firm than its market value.  The firm should reduce its capital stock (sell equipment, etc).

In both cases, diminishing marginal utility means q should tend toward 1.  If q>1 and a firm acquires more capital, average productivity will decrease until the market value of the next machine will equal the acquisition costs.  Firms are indifferent to paying \$1 for \$1 worth of equipment.  If q<1 and the firm sells capital, average productivity will rise until the market value of the remaining capital equals the replacement/sales price.  Firms are also indifferent to selling \$1 worth of equipment for \$1.

In q theory, a firm acts to maximize the present value of its after-tax net receipts.  A firm’s investment level is a function of its marginal q.  For the specifics of the theoretical model, and for the explicit relationship between marginal q and average q, see “Tobin’s Marginal q and Average q:  A Neoclassical Interpretation,” (Hayashi 1982).

Marginal q refers to the market-value-to-replacement-cost ratio of the next unit acquired.  This cannot actually be observed.  What can be observed is the firm’s average q, or the ratio of market value to acquisition cost for the firm’s entire existing capital stock.