Recent development in demand analysis, Microeconomics

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RECENT DEVELOPMENT IN DEMAND ANALYSIS:

For many years economic theorists analysed the optimal behaviour of consumers while econometricians estimated consumer demand and expenditure relations, with little communication between the two. Theorists would provide examples that were of little aid for empirical work, and econometricians would estimates relations that had little connection with the theory of utility maximisation. Fortunately, as days passed on, the gap between theory and empirical evidence has lessened, and a number of theoretically strong examples that allow empirical estimation have been developed. In this section we present one of such examples.  

127_RECENT DEVELOPMENT IN DEMAND ANALYSIS.png

with the domain q11 and q22. The  γ's may be interpreted as minimum subsistence quantities and are positive. The α's are also positive. Applying the positive monotonic transformation U' = U/(α +α ) we get,  

2426_RECENT DEVELOPMENT IN DEMAND ANALYSIS1.png

The coefficients β1 and β21+ β2 = 1) are called "share" parameters. The consumer's objective is to maximise her utility subject to budget constraint. So, she will try to solve the problem given below. 

2482_RECENT DEVELOPMENT IN DEMAND ANALYSIS2.png

We set Lagrange function of the above maximisation exercise as  

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and set its first partial derivatives equal to zero (we assume interior solution of this maximisation problem):  

954_RECENT DEVELOPMENT IN DEMAND ANALYSIS4.png

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It can be easily verified that the second order condition for the maximisation is satisfied. By evaluating the above three equation one can also find out that the marginal utility of income is decreasing. 

Solving the above equations for optimal quantities gives the demand functions,  

563_RECENT DEVELOPMENT IN DEMAND ANALYSIS6.png

Multiplying the first equation of the above two demand functions by p1 and the second by p2 we get the expenditure functions  

1646_RECENT DEVELOPMENT IN DEMAND ANALYSIS7.png

which are linear in income and prices, and thus suitable for linear regression analysis.  


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