effect that can accentuate or dampen the fundamental response to demand.<sup>21</sup>

## **Asymmetric Output Response to Shocks**

The response to price shocks described earlier is illustrated by Figure 2, which is calculated assuming a Cobb-Douglas production function, a borrowing allowance of zero and a specific set of parameters.<sup>22</sup> The first panel shows the behavior of a firm that has very low cash and capital and is always constrained. The last panel shows unconstrained optimal behavior. The middle panel shows the combination of the two when the firm switches from optimal to constrained behavior with increasing magnitudes of the price shock. In this example, the _Sometimes Constrained_ firm has enough cash to afford optimal inputs at the mean price level equal to one. The firm is not constrained for shocks below the mean and becomes constrained for shocks above the mean. First, note in Figure 2, that as shown above, capital reacts countercyclically when firms are always constrained, but procyclically when never constrained.

The second proposition is that constraints bind with increasing price and as a result, output response to positive will be different from negative changes in the price. The asymmetry captured by the middle panel of Figure 2 is driven by constraints binding when the firm wants to expand production and not binding when the firm contracts. The left and right panels of Figure 2 clearly show that when firms are credit constrained, output is much less responsive to prices. Figure 4 illustrates the output response to a positive shock using isovalue curves and budget lines. Take two firms that are both producing optimally at point A in Figure 4. One firm is never financially constrained - it has ample internal finance or access to external credit. The firm uses the optimal amount of capital and labor to determine output. The other firm is on the margin of being financially constrained.<sup>23</sup> A positive shock shifts the isovalue curve outward and beyond the budget set of the credit constrained firm. While the firm without constraints can increase output to point NFC, the constrained firm can only increase as far as point FC. Thus, under positive shocks, the output of the credit constrained firm responds less than that of the unconstrained firm.

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# **3 Loss in Producer Surplus, Inefficiency and Firm Growth**

Financial constraints cause suboptimal input levels and distort the efficient relative factor ratio in response to shocks. Both of these effects contribute to lower output levels, leading to losses in producer surplus. As future production is dependent on revenue, the loss in profits in turn affects firm growth over time. The effects of financial constraints are magnified as working capital constraints become binding exactly when good production opportunities arise. I simulate the working capital model and the standard investment model using Matlab to illustrate the effects of financial constraints on output levels, efficiency, profits and long term firm value and growth.

> 21For example, if the borrowing allowance increases with price, this is equivalent to an increase in cash - which is a change in income.

> 22Here, the figure is intended to motivate the theoretical results. The choice of parameters is discussed in more detail in Section 3 when the model is simulated to examine output inefficiencies and the growth of the firm over time.

> 23The firm is limited in the sense that it can only just afford to produce optimally at point A where the shock level is equal to one. For any shock greater than one, the firm will be constrained, just as in the middle panel of Figure 2.

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