Menu Cost

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Menu cost, a term which usually shows up when cost of inflations are of concern, is a common term in the model of New Keynesian Economics (NKE). NKE tries to explain why and how movements in nominal Aggregate Demand (AD) caused by changes in monetary policy, can affect real variables, i.e. real output. The fundamental explanation, which is also the central aspect of all Keynesian model, is “nominal rigidities”, sticky prices and wages. NKE says that the rationales behind these nominal rigidities are due to: (a) the existence of small costs of changing prices, also known as menu cost and (b) the existence of long-term contracts, which is explained by the staggered price models. NKE provides microeconomic foundations for Keynesian economics as it models the effects of these micro-based costs and rigidities and shows that under these assumptions monetary policy can have large real effects. Menu cost is the cost of changing the price of firm’s goods. In the NKE model, it is a source of price stickiness. There are many reasons why it is the source of price stickiness (Mishkin, 2012): (1) changing prices involves many hidden costs (2) Since collecting information is costly, firms and households engage in rational inattention by only making decisions about prices at infrequent intervals. Customers may not immediately notice the price reduction and that provides less incentive for firms to cut prices (3) Changing prices frequently may alienate customers. Aside from the reasons above, there are two major papers which discussed menu cost and why monopolists are reluctant to change prices, even in the fall of aggregate demand. Firstly, we start off with Akerlof and Yellen’s paper on assuming “near rationality” that is equivalent to rationality subject to second-order costs of taking decisions (Akerlof & Yellen, 1985) and an extension of the paper done by Blancard and Kiyotaki (Blanchard & Kiyotaki, 1987). We first consider a monopoly firm, i, which has a value of function of . is the firm’s utility function which depends on its own price, Pi and demand (Y=M/P), giving . The envelope theorem then says that

If P is already the profit-maximising price, there is no change in price P that could increase profits in terms of Vi for any given change in monetary supply. Hence, . The effects on equilibrium as “first order” change shows that a change in M on the value of the firm is the same whether or not the firm adjust its price optimally. The firm’s loss from not adjusting its price to the new profit-maximizing level in response to a shock in the nominal money supply is “second order” small. The “second order” menu cost (larger than the second-order loss in value) will prevent each firm from changing its price given other prices. P1

V(P0,M1)
P0
V(P,M0)
V(P,M1)
V(P,M)
Figure 1
V(P1,M1)
P1
V(P0,M1)
P0
V(P,M0)
V(P,M1)
V(P,M)
Figure 1
V(P1,M1)

A graphical interpretation to represent the theorem mentioned above is represented by Figure 1, which depicts the value functions of firms for M0 and M1, where the optimal price for M0 is P0 and the optimal price of M is P1. When there’s a decline in demand represented by M, the firm behaves inertially, leaving price at P0 will incur a loss, from failure to maximise at M1, equals to V(P1,M1)- V(P0,M1), which as shown by the graph is second order small. The intuitive explanation behind this is that the essential feature of optimal choice is indifference at the margin. (Akerlof & Yellen, 1985) The benefit of changing price may be very small compared to leaving it fixed at the old price, thus it makes sense that a small menu cost of changing prices might prevent price changes occurring. Next we consider the second major paper by Mankiw (1985) on the possibly large macroeconomic effects of sticky prices resulting from small menu cost. We first consider a monopolist firm facing a linear demand curve with constant Marginal Cost and no fixed costs, making MC=AC. Profit...
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