Ebook Quantity Adjustment Costs and Price Rigidity
In recent years a widespread explanation for price rigidity has been lump-sum costs of changing nominal prices, the socalled menu costs. As the name suggests these costs are considered to be small, but shown to have real effects in Mankiw (1985) and Blanchard and Kiyotaki (1987) among others.
The key point is that the loss of not adjusting prices to a given shock is only of second order smallness for the individual agent, whereas the aggregate effect is of first order. This also indicates that because it is not optimal for the single price setter to change its price, the price level may be rigid, and the shock (for instance a demand shock) may affect output causing real effects on welfare. The welfare consequenses of menu costs have been dealt with quite extensively. For an thorough and very good overview see Andersen (1994).
However, the effect on output might be an implication of there being no adjustment costs on quantities. If there were costs associated with changing quantities, output might not respond to a (demand) shock. Therefore, there is a bias against not adjusting prices in the menu cost models, as only price adjustment is thought to be costly. Hence it seems of vital importance to integrate both price and quantity adjustment costs, since it is by no means obvious at all that adjustment costs on quantities should be zero. Surprisingly, this has received almost no attention in literature with Andersen (1995) as the only exception, to my knowledge. He demonstrates how a single firm will choose optimally between adjusting either the price or the quantity or both in a static model with lump-sum costs of adjusting both the price and the quantity. It turns out that the mode of adjustment is not just the trivial one that bears the lowest costs of adjustment, other interesting implications emerge as well, such as rationing and asymmetric adjustment to positive and negative shocks.
However, in Andersen (1995) the adjustment costs for quantities are only of a lump-sum nature. This appears odd in the context of quantities. If for instance, you need to increase production, it seems natural that the costs of doing so increases with the size of production in excess of the ordinary marginal costs . For instance, over-time payment to the employees or new capital acquisition if you initially were at maximum capacity. Thus, in this paper the model by Andersen (1995) is extended by incorporating quantity adjustment costs that have both a linear and a lump sum component. Furthermore, the model is dynamic, allowing for an analysis of the firm’s response to both permanent and transitory shocks. These extensions alternate the conclusions reached in Andersen (1995) concerning the mode of adjustment.
One of the major new insights from incorporating linear adjustment costs is that prices seem to bear a relatively larger burden of adjustment when the shock is ‘large’, and quantities a relatively larger share when the shock is ‘small’. This has the important implication that for small shocks prices are sticky and the nominal rigidity has real effects; and this effect is an even larger effect than in the traditional menu cost models. Furthermore, the dynamic aspect contributes to interesting findings concerning the mode of adjustment. In particular, it will be demonstrated that even if it is more costly to adjust quantities, price rigidity may still be observed. Also, if the quantity adjustment costs involve a linear component on top of the lump-sum costs, price rigidity becomes more pronounced, even though price changes are now relatively cheaper. Thus, some of the critique levelled at the traditional menu costs models saying that there is an inherited bias against price stickiness, may in some cases not be justified.
These features relating to the dynamic aspect of the present paper, does by assumption not occur in Andersen (1995). However, the important findings concerning rationing and the asymmetric adjustment to positive and negative shocks remain.
The paper is organised as follows. In section 2 the basic model is set up. In section 3 we discuss the case of a permanent shock, in order to be able to study effects that pertain to the cost structure and not necessarily to the model being dynamic. Then we proceed to the dynamic case in section 4 where a temporary shock is considered. Finally section 5 concludes and discusses limitations of the results obtained.
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