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By Louis Philips, Lester D. Taylor (auth.), Louis Phlips, Lester D. Taylor (eds.)

During this testomony to the celebrated occupation of H.S. Houthakker a couple of Professor Houthakker's associates, former colleagues and previous scholars supply essays which construct upon and expand his many contributions to economics in aggregation, intake, progress and exchange. among the individual participants are Paul Samuelson, Werner Hildenbrand, John Muellbauer and Lester Telser. The booklet additionally contains 4 formerly unpublished papers and notes by way of its extraordinary dedicatee.

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Additional resources for Aggregation, Consumption and Trade: Essays in Honor of H.S. Houthakker

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N 1 also shows that, if for a given data set one wants to analyse whether the matrix B(f,p) is positive semi-definite, then one has not to estimate the crosssection demand function, provided one assumes that it is generated by a given collection of base functions. Indeed, one should investigate directly whether the matrix B(b,p) is positive semi-definite [Qr the estimated expenditure distribution. Only in the exceptional case where rank C < S, B(f,p) can be positive semi-definite without B(b,p) having this property.

We now want to come back to our claim that the shape of the cross-section Engel curves and the expenditure distribution play an important role for deriving the Law of Demand or the Weak Axiom of Revealed Preference. Under suitable assumptions on the consumption sector, one can show (for details see section 2 below and Hildenbrand (1991» that the Jacobian ~atrix 8 p F(p) is the difference of a negative semi-definite matrix and the following matrix A A= {f (8Jk(P,X))fj (p,X)P(X)dX)k,j =l, ... ,K .

However. the idea is that the number of base functions is small compared with the number of commodities (commodity aggregates). and that the base functions are chosen independently of the particular crosssection demand function. We allow the base functions to depend on the price system. but in the examples below we shall use base functions which only depend on the expenditure level x. Obviously. the acceptability of using few base functions is an empirical question. The restrictiveness of the assumption depends not only on the total number S of base functions.

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