# Production Function for a Retail Store

Estimation of Production function for a retail store.

Adapted from the article by Charles A.Ingene and Robert F. Lusch, www.emeraldinsight.com:

Retail is a growing sector and is also one where the effect of the global recession is visible. It is absolutely essential to ensure that the investments made here, as anywhere else, are well informed decisions ensuring its productivity at the highest level. It is important to ensure this because this is a significant component of the cost of marketing any good.

This exercise in estimation of a production function for departmental stores r was undertaken in the USA way back in 70s, when retailing in India had not yet been recognized as a significant component of marketing costs. The study enables the decision maker to construct a store of optimal size.

A production function gives the most efficient technical relationship between inputs and output for any given technology The specific form of the production for used here is the Cobb-Douglas production function. The equation fitted is of the form Q = A Kα Lβ ℮ Where Q is the output, A is the technology, K is the capital and L is the Labor , α and β are the elasticities.

The study uses cross-sectional data from the year 1972 for 245 standard Metropolitan Statistical Areas (SMSA). Output, in retail for a departmental store, includes many different physical items and services, and hence is measured in value terms expressed in dollar units. Q is therefore total department store sales in an SMSA divided by the number of department stores in that SMSA.

Labour was the average no. of hours of employee labour for each SMSA. One employee was equated to 2000 hours per year. For a measure of physical capital, the study uses the data available on total floor space. So the generalized C-D production function which was estimated was:

Sales per store Q = A Fα Lβ

The result is:

In Q = 2.265 + 0.172 In F +...

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