Lancastrian Demand Theory and Linier Expenditure function

Lancastrian demand theory was developed by Australian Economist Kelvin Lancaster. He published an article on Journal of Political Economics in 1966 entitled “A new approach in consumer theory” and also published a book called   “Consumer Demand: A new approach” in 1971.

According to Lancaster, A consumer chooses to buy a particular product not only because of its Utility and cost but based on the combination of attributes which includes Taste, color, size, weight, price, etc.

Thus, U = f ( Taste, color, price, weight, size, etc. )

He explained it further by taking in consideration of why an individual buys a particular food item.

Let consumer buy the food item based on two nutritional factors: Vitamin (a₁) and Calories (a₂). Suppose there are three items in consumption basket x, y and z.

Then,

a₁ = a₁^x x + a₁^yy+ a₁^zZ

a₂= a₂^xx+ a₂^yy + a₂^zZ

Where,

a₁^x= the vitamin obtained from good x

a₁^y= he vitamin obtained from good y

a₁^z=the vitamin obtained from good z

a₂^x = the calories obtained from good x

a₂^y = the calories obtained from good y

a₂^z = the calories obtained from good z.

The budget constraint determines the amount of good x, y and z to be bought looking at the attributes of these commodities or goods.

Suppose all income (i) is spent on commodity x, the Marshallian demand function from product x is x*=

Similarly, if all the income (i) is spent on commodity y, The Marshallian demand function from commodity y is y* =  

Therefore, a₁^x x* = a₁^x.  And a₂^xx* = a₂^x.

Therefore, the total demand of x will be based on Vitamin (a) and calories (b) obtained from the good x.

Similarly, If all the income is spent on good y, the demand will be y* and if all the income is spent on good z, the demand will be Z*.

If a consumer is willing to spend all his resource in commodity x, then he will spend at x*. If the consumer is willing to spend all his resource in commodity y, then he will spend at y*. Similarly, if he is willing to spend all his resource in commodity Z, he will spend his money in Z*. Similarly, if a consumer is willing to spend all his resource in commodity X* and Y* then he is willing to spend in x*y*. And the equilibrium level of his spending in these two commodity remains at E₁. Similarly, if a consumer is willing to spend his resource in commodity bundles y and Z then he will be consuming at equilibrium level y*.  Similarly, if consumer spends all his commodity in good x and good Z, he will remain at the point adjoining x* and Z*. There situations are presented in the graph below.

 

Commodity bundles demanded by the consumer