■ Tobin's q
It's known to all that q summarizes all the information about the future that's relevant to the firm's investment decision.
Actually q shows how the additional value of Nrs of capital affects the present value of the profits. Thus the firm wants to increase its stock capital q is high and reduce it if q is low. This implies it doesn't need to know anything about the future other than the information that is summarized in q in order to make this decision.
Romar stresses that the q has natural interpretation. Any one unit increase in the firms capital stock increases the present value of the firm's profit by q.
Similarly, it raises the value of the firm also by q. Hence q is the market value of the unit of capital.
If there's a market for shares in firm, for example the total value of the firm which one more unit of capital then other firm exceeds the value of the other firm by q.
To note, we also have assumed that the purchase price of the capital is fixed, q is also the ratio of the market value of a unit of capital to its replacement costs.
We state the firm increases its capital stock if the market value of the capital exceeds what is costs to acquire it, and decreases it's capital stock if the market value of the capital is less than what it costs acquire it.
Simply, the ratio of market value to the replacement costs of capital is known as Tobin's q.
The analysis implies that what is relevant to investment is the marginal q - the ratio of market value of the marginal unit of capital to its replacement costs.
The marginal q is more difficult to measure than the average q - the ratio of the total value of the firm to the replacement costs of its total capital stock. The the relationship between marginal q and average q must be known significantly.
Sometimes, in the model there would be that the marginal q is less than the average q. The reason maybe that when the adjustment costs depending only on k was assumed, means that the diminishing return to scale in adjustment costs was there.
Due to this assumption of the diminishing returns, firm's lifetime profit (pi) rise less than proportionately with their capital stocks and thus the marginal q is less than the average q.
Now, if in case we happen to modify the model into the constant returns to scale in the adjustment costs average and marginal q are equal , Hayashi (1982).
This implies that the q determines the growth rate of the firm's capital stock on CRS. With this firm choose the same growth rate of their as their capital stock.
For instance, say a firm has initially twice as much capital as another and if both profits optimize, the larger firm will have twice as much capital at every future time.
In addition to this profits are linear to the firms capital stock, this implies that the present value of the firm's profit, the value of (pi) when it chooses the path of its capital stock optimally, is proportional to the initial capital stock. Hence, in this case the average q and marginal q are equal.
Now, in other models there are potentially more significant reasons than the degree of returns to scale the adjustment costs, then the average q may differ from the marginal q.
Say if a firm faces a downward facing demand curve for its product for example, doubling its capital stock likely to less than double the present value of its profit. Hence, marginal q is less than the average q.
Say, if in case a firm owns a large amount of outmoded capital it's marginal q definitely exceeds the average q.
Thank You
Aditya Pokhrel
MBA, MA Economics, MPA
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