 And in this module, today we are going to study the consumer behavior and how the consumer is going to maximize his utility. Generally we have studied that the consumer is going to purchase two commodities X1 and X2 at their respective prices and at the point of tangent he is going to maximize his utility. But either this situation prevails throughout the situations or either there can be a different situation. So today's lecture is particularly related to that special case when the consumer is not having a preference for the two commodities because generally we say that the consumer is indifferent about various bundles of two commodities X1 and X2 along the his utility curve or along the indifference curve. But when he will not be indifferent and he is having a particular preference for only one commodity then this condition will be different. So keeping in view this special condition we say this as a corner solution and now coming to this we see that mostly the consumer is having a situation when he has to maximize his utility and for the maximize of utility he is generally having this equation where commodity one commodity or there can be the various other commodities subject to the condition that he is going to spend the whole budget where M is his income and that income is either equal to all the expenditure or might be somewhat access to that expenditure. So when the Lagrange multiplier is utilized and to the first order condition we differentiate this maximization equation with respect to change in one commodity and then we calculate that according to this now this lambda is equal to change in utility due to the change in price. So here the lambda it tells that when the price of one commodity will change in response to that change in price what will be the change in the utility and pertaining to this we can calculate that what will be the amount of that commodity demanded. And now if the consumer will be having preference only for one commodity then the equation will be different. And when the equation of the will be different in that sense that at tangency we generally has assumed that there is a relationship that tells that utility of first commodity it is divided by its own price is equal to the ratio of the utility with its that price and that is equal to U M mean here it is the utility of the money. So when tangency condition is not followed now that tells that now the total amount of this income will not be utilized for both the commodities rather it will be utilized all on only one commodity. When it will be utilized only on one commodity then the equation will be like this that either due to the change in the price of the commodity the change in the utility for one commodity will be more as compared to the other and keeping in view the marginal utility of expenditure or of income on that good that is very particular one is less than the marginal utility of money at the optimal point that is lambda. And when this situation then that good will not be bought since the consumer will get greater utility by expenditure on the other good and likewise the same result we can calculate for either other good means if we are having two goods X1 and X2 we can calculate one corner solution for commodity X1 and likewise we can calculate for X2 and if it is like this we have to draw the situation that if consumer is having one budget line like this and this budget line tells that here the income is equal to price of X1 into X1 plus price of X2 into X2 and keeping in view now generally before we were having this tangency solution but in the corner what we will be having it will be like this that there is budget but the consumer is not having any tangency rather it will be having various indifference curve and those indifference curve will be mostly touching this budget line only and only this point where there is X and likewise when the consumer is having the preference for the commodity X2 then at first indifference curve if consumer is utilizing the whole income to purchase only this amount X2 whenever he will be having more income or he is having any change in the price if there will be situation of income then this budget line will shift but if there is a situation only and only of the price change so whatever is the change in the price it will consume all of its total income for the purchase of commodity good X2 here if the budget will shift then there is a possibility that the consumer will shift from this position but if again his preference is for corner solution its intercept will shift but again with the same corner solution preference exhibition thank you