When Customers Arrive with Less Purchasing Power
This chapter follows the consumer-demand side of firm-level uncertainty: what happens when firms must choose labor and productive capacity before they know how many customers will arrive or how much those customers can spend. The useful judgment is not simply that tighter consumer credit lowers sales. It is that credit changes the distribution of possible sales per worker, and a capacity constraint determines whether that distribution becomes narrower or riskier.
The mechanism comes from a specific sequence. Firms commit to labor first. Customer matching and purchasing occur afterward. Wages and other balances are settled only after production and sales have been realized. That sequence turns purchasing power into an input to the firm’s risk calculation. It also shows why the phrase “demand shock” is incomplete: the shock can move both the average level of demand and the uncertainty surrounding an individual firm’s outcome.
The hiring decision comes before the customer decision
The Federal Reserve model divides each period into three stages. First, a firm chooses its labor input and sets the productive capacity associated with those workers. At that moment, the firm knows the prevailing aggregate consumer-credit condition, but it does not yet know the particular customer realization it will receive. The wage rate is not contingent on that realization, so the promised wage bill is fixed before actual sales are known.
Second, households are randomly distributed among producers and shop for consumption goods. Each household visits a limited number of producers, and the distribution across producers is not uniform. One firm may receive more customers per worker than another firm even though both face the same economy-wide credit condition. The customers also differ in the amount they can spend during this intra-period shopping stage. Their purchasing capacity is the channel through which aggregate consumer credit reaches the firm.
The aggregate condition is common, but its effect is not. A lower credit limit does not assign the same number of customers to every producer, nor does it make every customer spend exactly the same amount. It lowers the spending capacity available at each customer visit while the random matching process continues to distribute customers unevenly. The firm therefore faces two kinds of variation at once: a common change in the purchasing power of the market and an idiosyncratic realization of how many customers are available to its workers.
Third, wages and credit or debit positions are settled. Households can re-trade goods in a centralized market, and the entrepreneur makes the next saving or consumption decision after observing the realized sales outcome. The important asymmetry is therefore temporal: the firm commits resources before the demand realization, but it can adjust its financial position only after the uncertainty has materialized.
The later re-trading opportunity does not erase the firm’s lost sale. It can help households end the period with a more even allocation of goods, but it does not send a new customer to the producer that was under-matched, and it does not refund the wage commitment that was made before matching. The firm’s revenue and the worker’s production opportunity have already been determined in the shopping stage. This is why the model treats the timing of information as economically meaningful rather than as a technical ordering of events.
This is not a description of every retail or industrial market. It is a deliberately spare model of an information problem. The product is homogeneous and non-storable, labor markets are competitive, firms have only a non-contingent bond to help insure idiosyncratic risk, and the baseline contains no default. Those assumptions remove many institutional details so that one relationship is visible: hiring is a bet on future customer purchasing power.
That information order also distinguishes a trigger from a mediator. The aggregate credit condition is the trigger. Random customer matching and customer spending capacity mediate its effect on realized sales. The firm’s capacity choice determines which part of the demand distribution can be converted into revenue. The eventual employment and output response is an outcome of all three, not a direct mechanical response to a credit statistic.
A useful way to read the sequence is to separate what the firm knows from what the firm controls. It observes the aggregate credit environment before choosing labor. It controls the number of workers and therefore the amount it could produce. It does not control the number of customers assigned to it or the purchasing capacity those customers bring. After the shopping stage, it observes the outcome but cannot use that information to undo the earlier hiring choice. The uncertainty is consequently not just a forecast error in an analyst’s spreadsheet; it is a constraint on an irreversible—or at least already costly—operating commitment within the period.
A capacity ceiling changes the shape of sales
The model’s sales rule can be stated without the notation. Sales per worker equal the smaller of two quantities: the firm’s technological capacity per worker, and the purchasing capacity delivered by the customers assigned to that worker. In shorthand:
Sales per worker = the lesser of capacity and customers per worker × purchasing capacity per customer.
The first term is a ceiling. No matter how much purchasing power a customer brings, a worker cannot produce more than the per-worker capacity. The second term is a demand limit. If customers bring too little purchasing power, the firm cannot sell all that the worker could produce. This “minimum” is what makes a change in credit conditions affect dispersion as well as the mean.
Consider a purely illustrative worker whose capacity is 10 units. Under a high purchasing-capacity condition, one well-funded customer might be able to demand all 10 units, while several less-funded customers could together do the same. Once demand reaches 10, their different purchasing capacities no longer create different sales outcomes: the capacity ceiling makes them look alike from the firm’s perspective. Under a low purchasing-capacity condition, each customer can buy less. A worker may then need many customers to reach 10 units, and a worker who happens to receive fewer customers will record a much lower sale. The example is not an estimated parameterization; it isolates the nonlinear role of the ceiling.
The same example can be viewed across two firms rather than across two customers. Suppose both firms employ one worker and have capacity 10. In a high-credit state, Firm A’s two customers and Firm B’s five customers may both generate enough purchasing power to fill capacity. Their realized sales are then similar despite different customer counts. In a low-credit state, those same customer counts may no longer be sufficient to fill capacity. Firm B can still sell more than Firm A, while Firm A’s sales fall sharply because its small customer pool now carries less spending power. A common credit change has exposed the firms’ different customer realizations.
This produces two effects from one aggregate change. The first is a first-moment effect, meaning a change in expected sales. When customers have more purchasing capacity, the firm expects higher sales per worker. When their capacity falls, the expected level falls. This is the ordinary demand channel and would exist even in a model where the shape of the distribution did not change.
The second is a second-moment effect, meaning a change in dispersion or risk. Better customer credit raises the spending of low-capacity customers and pushes more realizations toward the common production ceiling. The distribution of sales per worker becomes more compressed in the relevant region. Worse credit moves the other way. High-capacity customers may still be able to support substantial sales, but low-capacity customers no longer do so, and the number of customers required to make a worker profitable rises. The gap between strong and weak realizations widens.
The direction can be understood as a censoring problem. A capacity ceiling cuts off the upper part of the sales distribution. When purchasing capacity is high, more potential outcomes are cut off at the same ceiling. When purchasing capacity is low, fewer outcomes reach that ceiling, so the lower-demand portion of the distribution matters more. The aggregate shock has not merely shifted every firm’s sales left or right. It has changed which outcomes remain exposed to customer heterogeneity.
This also explains a result that can seem counterintuitive at first. Better credit may cause more firms to operate at their capacity ceiling even though it reduces the dispersion of sales per worker. Capacity utilization and uncertainty are not opposites here. A firm can be more likely to sell everything its workers can produce while facing less uncertainty about the next worker’s revenue, because many customer realizations now produce the same capped outcome. Under tighter credit, fewer firms reach the ceiling, but their sales become more dependent on the particular number and purchasing capacity of the customers they happen to receive.
The distinction between a shift and a reshaping is important. If the credit condition simply moved every firm’s sales down by the same amount, the relative ordering of possible outcomes would remain much the same. The capacity rule changes that ordering at the margin. A formerly adequate customer pool may become inadequate, while a high-purchasing-power pool still fills capacity. Some firms are pushed into the exposed part of the distribution; others remain protected by enough customer spending to stay at the ceiling.
This is why better credit can make hiring safer even before a firm has hired another worker. The firm’s expected marginal worker is evaluated over a distribution of possible customer outcomes. If that distribution is compressed by the capacity margin, the downside attached to the wage commitment is smaller. Under tighter customer credit, the same wage commitment is exposed to a wider range of realized sales. The hiring decision will be discussed in full later; the present point is that the risk enters before production, through the shape of possible revenue.
The mechanism depends on the capacity margin. If the ceiling is so high that almost no firm reaches it, improved customer credit mostly raises sales per worker and leaves dispersion less affected. If many firms are close to capacity, the same credit change can move a large amount of probability mass against the ceiling and materially compress uncertainty. The size of the second-moment effect is therefore state-dependent, not a universal percentage attached to every consumer-credit shock.
Why the distinction matters for firm-level uncertainty
The model gives “uncertainty” a precise place in the firm’s decision problem. It is not simply a feeling that the economy is unstable, and it is not identical to a volatility index. It is the dispersion of sales outcomes that a firm must consider when labor is chosen before customer demand is realized. Aggregate consumer credit changes that dispersion because it changes each customer’s spending capacity and interacts with the firm’s capacity limit.
The distinction also prevents a common analytical error. If a firm sells less because every customer has less purchasing power, that is a lower expected-demand response. If the firm becomes less willing to commit to labor because the possible sales outcomes are farther apart, that is a risk response. The two can happen together, but they answer different questions. The first asks how much revenue the firm expects. The second asks how much downside the firm must be prepared to absorb around that expectation.
The customer distribution also should not be confused with a claim that every firm knows nothing about its market. The model abstracts from firm-specific information about repeat customers, contracts, prices, and inventories. Its point is narrower: even with a common aggregate credit condition and a known distribution of customer behavior, the realization assigned to one firm can be uncertain at the moment labor is chosen. Adding better information or contingent contracts could reduce the effect. Adding more rigid capacity or longer commitments could strengthen it. The model identifies the direction of pressure under its stated structure; it does not determine the size of the response in an industry with different institutions.
The Federal Reserve paper uses this structure to connect consumer demand to the cross-sectional facts reported in U.S. firm data. Its calibrated model is not intended to reproduce every contract or pricing practice. It is intended to show how a relatively simple capacity-and-matching mechanism can generate countercyclical dispersion in sales outcomes and a plausible connection between credit conditions, firm hiring, and aggregate activity.
The essential ingredients are consequently clear. Customer purchasing capacity must vary with the aggregate credit condition. Customer assignments must be heterogeneous enough to create different firm outcomes. Firms must commit labor before learning the relevant customer realization. And productive capacity must bind for at least some firms, so that better purchasing power compresses some outcomes while tighter purchasing power exposes more of the lower tail. Remove any one of those ingredients and the mechanism changes, sometimes substantially.
The remaining question is behavioral. A wider distribution matters only if someone must choose under it. The next step is to examine the risk-averse owner who compares higher expected sales with a wage bill that must be paid even when customers arrive with too little purchasing power. That is where firm-level uncertainty becomes lower hiring and output rather than merely a wider chart.