Daryl Chris asks:
Consider a price-taking profit maximizing business in perfect competition. The market is in equilibrium and each business is producing at its MES (making just normal profit). Each firm uses just two factors of production: labour, which is the variable factor, and capital which, in the short run, is fixed.
Now suppose that the interest rate (which you may treat as the cost of capital) rises. You may assume that, in consequence, the MES falls. Explain and analyze the consequences of the change in the cost of capital, distinguishing carefully between short and long run effects. Explain the nature of new long-run equilibrium (in terms of output at the level of individual business, price & output in the market place, and the number of firms in the industry). In explaining the new equilibrium and its differences from the original equilibrium, describe and analyze carefully the transition between the two equilibria.
I am having difficultly tackling this question.
The immediate effect of the rise in interest rates is to increase the cost of capital for all firms in the industry. Marginal cost is unaffected since capital is a fixed factor, but average cost will rise. Since firms were originally making normal profits, the effect is that they now make sub-normal profits - i.e. losses. A firm will remain in the industry so long as price is at least equal to average variable costs. Since there is no reason to suppose that all firms' AVC are equal (since they are likely to be using different combinations of capital and labour) some firms will find that price is now below AVC and will therefore leave the industry. Hence the output of the industry as a whole will be lower than previously.
The effect of a lower output for the industry as a whole is to shift the industry's supply curve to the left. This in turn increases the price that prevails in the industry, thus increasing average and marginal revenue (which are of course equal) for all firms in the industry. This means that some firms that remain in the industry may now be making super normal profits, wherever their AR exceeds AC at the MC equals MR profit-maximising output. The output of such firms will have increased. Firms will also seek to minimise costs, wherever possible, by substituting labour for capital; this will have the effect of lowering their average costs in the long run, and thus increasing SNP. The SNP made by some firms will now attract new firms into the industry, the effect of which is to increase the output of the industry, and thus lower the price that each firm (all are price-takers) can charge. The output for an existing individual firm will therefore be reduced. At the same time, firms will seek to employ the most efficient combination of factors with a view to lowering average costs in line with the most successful firms. Hence, and making the critical assumption of perfect knowledge (and perfect mobility of factors in the long run) all firms in the industry should end up with identical cost curves. Given that they are all charging the same price, the processes of new firms entering the industry and of changing factor combinations employed will come to an end when all firms in the industry are making normal profits only - i.e. where price equals AC. The industry will then be in long-run equilibrium.
I hope this is helpful.