Increases in interest rates due to bank capital scarcity cannot generally lead to increases in prices, because interest rates are the arbiters of general employment levels which in turn control demand for goods. However, changes in interest rates can precipitate changes to market structure that cause increases in the cost of goods in individual markets, or occasionally precipitate both unemployment and inflation, given that economic growth within a region is sufficiently robust or the general population is sufficiently wealthy. To illustrate, begin with the following example of a single firm within a single industry.
Imperial Widgets (IW) is a widget factory facing capital replacement costs due to depreciation. The company is not profitable (zero net profit) and has no liquid assets that can be sold to finance such a purchase. Therefore, the company must take a loan to cover these replacement costs or cease operations. Supposing that IW takes such loans on a rolling basis and therefore faces similar monthly payments (without loss of generality) in each term.
Further, suppose that IW is making its price and quantity production decisions in a competent fashion, that is to say it is maximizing (or attempting to maximize) its profits. It expects an increase in price charged to lead to a decrease in sales sufficiently large to reduce profits and a decrease in price charged to similarly lead to an insufficiently higher volume of sales; additionally it is not likely to sell additional units produced, the marginal cost of production equals the marginal revenue, or IW is already producing at capacity. In other words, IW's profits would decline were it to maintain current capital stocks but change its price and/or quantity of production.
Now, suppose that interest rates increase. As IW considers its replacement schedule for depreciating capital, it realizes that it faces a change to its cost curve that could alter its price and quantity decisions. Depending on the capital objects to be replaced, IW may either curtail production and increase prices, or simply operate at a loss. In the first case, IW is likely to only obtain a partial replacement of capital, thus it is borrowing less. In the second case, IW is likely to finance these losses, causing an increase in borrowing.
The distribution between these two decisions across all firms is connected in a mutually causative way with the economic trend. At the macro level, some firms will move in one direction and some firms will move in the other, but a third option looms in the shadows. Here, long term expectations become significant - do firms that are operating at a loss hold out for better days or close shop? In any event, employment declines so long as at least one firm either cuts production or goes out of business.
The model case from here on will depend on market structure. It is virtually impossible to conceive of a monopoly enterprise that is not in the first place profitable, so we can focus instead on competitive and near-competitive markets. Within such a market some firms will be facing slightly higher cost curves and others slightly lower curves, but all firms will charge very similar prices for the same good, therefore some firms will be slightly profitable or have liquid asset reserves and some will be operating at a slight loss or have a deficiency in liquid asset reserves. When interest rates increase, some firms will face untenable finance positions and close. Therefore, interest rate increases can cause the breakdown of competitive market structures and lead to monopoly, cartel, or other degenerate market structures. This in turn allows the individual market to come to a higher price equilibrium due to the diminished competition within the market. This higher price equilibrium is generally accompanied by lower output.
However, if similar effects occur across too many markets at the same time, the reduction in employment level and wages that accompanies such restructuring leads to decreases in demand for goods through both revision of consumer budgets and increased incentives to save. In such a situation, the prices charged for goods must decrease as output declines, because prices follow a cost curve that is non-horizontal (due not just to the initial assumption of high interest rates and capital scarcity but also to the reduction in wages). A reduced output level must in turn exert downward pressure on interest rates.
Another under-appreciated aspect of this problem is the role that investment decisions play in the availability of capital to banks. Bank loans are a class of investment that competes with direct investment in corporations. During boom times, the increase of direct investment in corporations is a source of the very capital scarcity that leads to market consolidations as described above. However, during more stagnant economic times, companies cannot raise capital as easily because of the greater risk associated with direct investment. This means that capital is being held in bank accounts, implying a capital surplus - so interest rates should tend to fall as economic conditions deteriorate.
Economies go into crisis when prospects for direct investment become so bleak that essentially no direct investment occurs. Here, individuals will even settle for no interest and keep money in the bank, waiting for better times. These better times are caused by exogenous effects - technologies, government stimulus, and resource discoveries.
In contrast, economies also go into crisis when too few dollars are available for loans. If spending is sufficiently robust, investors will be unwilling to leave any money sitting. Capital for short term adjustments becomes too expensive for firms, and they are forced to curtail production. During times of especially strong demand, this can lead to prices increasing even as unemployment increases. Ultimately, the ability to spend is actually a function of wealth and not of income. Among other things, this explains the enigmatic "stagflation" of the 1970s.
In a previous post I have described these two contrasting situations as "disincentive" and "shortage". It is "shortage" that most closely corresponds with bank capital scarcity scenarios particularly the enigma of stagflation.
It is worth addressing whether such an effect - stagflation - can occur in a less developed country (I cringe and the imperialist heritage of this term. Is it conceptually much different than "less civilized" or "barbarian"?) due to the same forces as in a developed one. Here, banking and capital sources are primarily externally located. This is crucial, because it implies that any growth or decline in local demand will only have a marginal effect on the investing economy. These export economies do not get the benefit of profit capture or control, because the investors are not members of the economy itself and do not have a stake in the local community. It is the destabilization that the interests of the foreign investor bring to the political process that repeatedly dooms efforts at growth and social justice within a developing country. Generally, both loans and direct investment will always be available or unavailable in parity to the developing nation. It is not some economic law - but the political conditions of our time - that leads to suffering throughout the world.