Abstract
Dynamic models of the firm applied to market intermediary behavior are reviewed and formulated. An important input that we have ignored so far is capital. Different models applicable to modeling capital, with special reference to agricultural models, are presented and discussed in this chapter. Both single capital input and multi-variate adjustment cost models are presented. The linkage between quasi-fixed inputs and raw material demand is highlighted. Inventories can be a source of dynamic adjustment of the firm. Dynamic inventory models are formulated to show how lagged inventory adjustment can lead to lagged adjustment in prices and input demands. I discuss some ways in which this model can be modified and extended for other applications. Expectations and lagged inventories through adjustment costs are shown to be significant factors in dynamic adjustment. Different models for expectations formation are presented, and the dynamic inventory model is specified for quasi-rational expectations. Other, mostly empirical approaches to modeling dynamic input demand behavior are also discussed.
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Notes
- 1.
Lucas (1976b) defines the production function with respect to gross investment as opposed to net investment. Subsequent applications are almost exclusively in terms of net investment.
- 2.
To simplify notation, the time dependence of all variables has been suppressed.
- 3.
Factor prices are prices relative to output price.
- 4.
To simplify the notation, the constant \(g_{0}\) has been omitted. It has no consequence for the final equation derived.
- 5.
All the terms in the quadratic function are not included (e.g., squared input prices), because they do not show up in the optimization results.
- 6.
In the general case, where the sum of coefficients on all lagged variables, (\(\sum a_{i} )\), does not sum to one, as in the case of I(1) time series, the sales expectation model can be shown to equal \(E_{t} x_{t + j} = \left( {\sum a_{i} } \right)^{j} x_{t - 1} + \left( {\sum a_{i} } \right)^{j} \varvec{e}_{1}^{\varvec{'}} \varvec{A\iota }\left( {\varvec{I} + \frac{1}{{\sum a_{i} }}\varvec{A} + \frac{1}{{\left( {\sum a_{i} } \right)^{2} }}\varvec{A}^{2} + \ldots \frac{1}{{\left( {\sum a_{i} } \right)^{j} }}\varvec{A}^{j} } \right)\Delta \varvec{X}_{t - 1} =\left( {\sum a_{i} } \right)^{j} x_{t - 1} + \left( {\sum a_{i} } \right)^{j}\varvec{e}_{1}^{\varvec{'}} \varvec{A\iota }\left( {\varvec{I} - \frac{1}{{\sum a_{i} }}\varvec{A}} \right)^{ - 1} \left( {\varvec{I} - \frac{1}{{\left( {\sum a_{i} } \right)^{j} }}\varvec{A}^{j} } \right)\Delta \varvec{X}_{t - 1}\), where \(\Delta \varvec{X}_{t - 1} = \left( {\Delta x_{t - 1,} ,\Delta x_{t - 2,} , \ldots \Delta x_{t - 1 - n,} } \right)^{\varvec{'}}\) as before and \(\varvec{\iota}= \left( {1,1, \ldots ,1} \right)^{\varvec{'}}\). The price expectations model would have a similar form.
- 7.
- 8.
Because this study was conducted before the methodology put forth here, it was based on the same methodology of Lopez (1985) where expectations were assumed to be static. Also, the expected demand function was modeled as a function of the firm’s price, expected industry price, and expected industry demand. Thus, there were two demand shift variables, expected price modeled as lagged price, and expected industry demand modeled as lagged wine shipments for periods t-1 and t-2.
- 9.
See Labys (1973) for an extensive discussion of commodity models with inventory and trade variables.
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Wohlgenant, M.K. (2021). Dynamic Models of the Firm. In: Market Interrelationships and Applied Demand Analysis. Palgrave Studies in Agricultural Economics and Food Policy(). Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-030-73144-1_10
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