 Marchelian demand function. What is the Marchelian demand function? It means the consumer demand was studied then that particular behavior that was explained by Dr. John Marshall that was described in 1884 that was called particularly the Marchelian demand function. So the Marchelian demand function is basically a mathematical relationship that relates the price of the good demanded to its price and at the same time we can say that it shows the quantities demanded of the good at various times and at various places and at various price of the same commodity but holding the income and the price of the other goods constant. As we know that the change in the price it will change the purchasing power of the consumer. So when the purchasing power of the consumer it will become in the way that if the price has increased it means decline in the purchasing power. If price of the commodity has decreased it means the total purchasing power of the consumer has increased. Or if I want to say in this way it will be that when the price of a thing is decreasing then the income of the consumer increases but the lower the price of the product the more the unit was buying if the price of a thing is 10 rupees and it had allocated budget it had kept that I have bought 6 units then it took 60 rupees but as soon as the price of the commodity is 8 rupees instead of 10 rupees and it buys only 6 units then now it is possible for the consumer that it will buy the same unit but in 48 rupees. This means that now the consumer has left 12 rupees out of the last 6 rupees. This is now an incremental addition to the purchasing power. Similarly when the change in price increases then its opportunity cost of purchase reduces because of its purchasing power keeping the nominal income constant. In this concept when we say the marshalian demand so we do not compensate for the change in purchasing power. Means if its purchasing power of the consumer decreases then it is not given extra amount to compensate for it. And if its purchasing power increases means the real income does not take it back. So marshalian demand function may nominal income it remains constant. So this marshalian demand function is also called uncompensated demand function. And marshalian demand function which provides solution through the indirect utility function. Now if we look at the indirect utility function it tells that in the marshalian demand curve consumer attains the utility not through the utilization of a commodity rather he attains the utility through the consumption or the expenditure on the commodity. Means the consumption of the consumer is spent on its amount and gets a kind of utility. Means because that expenditure or expenditure which the consumer is doing to attain its demand is not possible for us to exceed its income under the law of budget. So it means we can assess the demand behavior not only from the side of the commodity quantity rather we can measure or we can assess also through the change in the expenditure utilize to attain that quantity. So it is possible to solve the necessary conditions of a utility maximization. So when we are dealing with the utility maximization we already know that the consumer is always in a better way utilizing not only one good rather he prefers to utilize a complete bundle. So in this case now the optimal level that the consumer is having that is amount of various combination of the x commodity that is 1, 2 and up to n mean it is the multi good case and when it is expressed in the form of mathematical notation we can have that now the consumer is having the demand function that depends upon the price of x and price of 2, 3, 4, 5 and the income of the consumer. Now if we will see the demand function for the commodity 2 it will again will be similar and like this we can have any sort of the demand function for any commodity depending upon the prices of all the commodities and the income of the consumer. But now we see for the simplicity if we take only two commodities we can say now that these are the different forms of the demand functions and now these demand they depend upon the values of all the prices and now we can predict that how much of this x commodity it can a consumer can attain with the change in his expenditure with the change in the price. So when we have to calculate this we can see that number one there will be this demand function and this demand curve is expressed holding the prices of this price and income constant and even the preferences or all the other taste constant so we will put a bar up to this and when we include this only the change of one price to this it means that is the partial equilibrium analysis keeping all other things constant. So either we are dealing with the two good case either we are dealing with the multi good case whatever but at that particular time of the analysis we will deal with only one change of that commodity keeping all other factors constant that's why this Marshallian demand function is also called partial equilibrium analysis and the partial equilibrium analysis approach and sometime it is also called walrus analysis or the walrus approach similar to walrus when we are dealing with the general equilibrium model.