noc18-mg22-Lec 16-Price Consumption Curve & Related issues

[Music] [Music] hello welcome back to the lecture series on microeconomics let us continue with the discussion of comparative statics in the context of a consumers equilibrium now we are going to introduce a concept called price consumption curve which will display another type of comparative statics analysis and these comparative statics our analysis are due to change in prices so in that case we get what is known as price consumption curve so a price consumption curve is basically the locus of consumer equilibrium points with varying price level of one commodity with constant money income and constant price of the other commodity this is abbreviated as P si si so now let us have a quick look at the diagram which will find the price consumption curve so we can assume price of commodity one has gone down while the price of the other commodity stays constant and money income does not change either now let's look at the graph so let us start with an initial budget line now if price of commodity one Falls then what do we expect we know that the slope of the absolute value of the slope of budget line is the relative price ratio right so if P one Falls then basically the budget line will become a flatter one so we are going to deal with a flatter budget line so the budget line will rotate from its intercept on x2 axis and it will have a higher intercept on the X 1 axis because with a lower price of commodity 1 the consumer is permitted to purchase more units of commodity 1 now of course we are going to superimpose the indifference map on this budget line diagram so the consumers equilibrium is going to be obtained at the tangency point as we have done earlier also now there will be another tangency point here and if we assume further price falls then we can have more flat budget lines like this one and then of course we can have another indifference curve and another tangency point like this so now the price consumption curve will start from this initial intercept of the budget line the intercept on the y axis or the x2 axis and it will move downwards it will join all these created equilibrium points and locus of this new consumer equilibrium points is called price consumption curve so now we are going to assume price of commodity one to go up while the price of the other commodity stays constant and money income does not change either now let's look at the graph so we start with the initial budget line say a B so with a high price the consumer will be able to purchase lower units of commodity one so that means we are expecting a lower level of intercept along the axis of commodity one so with a price rise the budget line will now rotate from this point a it will rotate inwards and this time it will create a lower intercept along the X 1 axis what will happen on the optimal consumption level of commodity 1 and community two to see that we have to superimpose the indifference map so let us start with this initial level of utility and this is the level of utility that the consumer used to get when the price was lower price of commodity 1 was lower and you can see this will be like X star 1 and X star 2 now note as the price of commodity 1 has gone up the relative price ratio has actually gone up so the budget line has become steeper right so this a B line a B Prime new budget line is a steeper budget line so this is the old or previous budget line and this one is new budget line so as the budget line has become steeper the new budget line a B prime will make tangency with another indifference curve say u 1 and the new equilibrium point could be this so let me name this e 2 the second equilibrium let me name the first equilibrium is e 1 so here you can see as the price of commodity 1 has gone up there is an impact on the consumption of both the goods new level of commodity consumptions are X 1 double star and X 2 double star if there is a further shift so if there is a further rise in price of community 1 then the budget line will become even more steeper and we we'll get a lower intercept a and the new budget line will be a be double prime so we are expecting another tangency point to the indifference curve with this new budget line something like this we can say this is utility level 2 and here is where the new equilibrium is its equilibrium e3 so one can see that at this new optimal choice made by the consumer the consumer actually has lowered the consumption of both the commodities now the commodity ones consumption has gone down to X 1 triple star and the consumption of 2 has gone down to X 2 triple star as well now to generate price consumption curve one has to join these equilibrium points we have to start from this point a because if price of one is so high then the consumer may not be able to purchase any unit of commodity one so it has to start from that point a and then it will come down words it will touch III and it will pass through e 2 and E 1 and then move upward so price consumption curve is basically the locus of all equilibrium points when price of a commodity change we have obtained price consumption curve from varying the budget line of a consumer now we are going to study various shapes of price consumption curve note that price consumption curve always will start from the intercept along the vertical axis because if the price of commodity 1 is infinitely high then the consumer will not purchase even a single unit of commodity one he or she will spend the entire money on commodity 2 after that if price of one Falls then the consumer will divert some amount of money from consumption of 2 towards consumption of 1 and hence consumption of commodity too will fall and consumption of community will keep on increasing so initially the price consumption curve will always be downward sloping but does it mean that the price consumption curve is downward sloping all the times the answer is no so depending upon various values of own price elasticity the price consumption curve can take various shapes now we are going to study for such cases so now we are going to study shapes of price consumption curve and throughout this analysis we are going to assume that price of commodity one has fallen price of commodity 2 remains same and money income also remains the same so now let us list down these cases one by one case number 1 which is forward bending bcc so just in this case I am going to draw the indifference curve and the budget lines in great detail to save time in the next cases I am only going to draw the final shape of PCC so please note how I am going to draw so let us start with the initial budget line say a B then suppose there are price falls for commodity 1 so after first round of price fall the budget line becomes flatter and the budget line becomes a B prime so the budget line rotates along Point a now there is a further fall in price of commodity 1 budget line becomes even more flatter and we get a B double prime as the budget line now as the price keeps on falling the budget lines will create new tangency point with the indifference curves right so now let us go into superimpose these indifference curves so the initial budget line a B makes a tangency with this indifference curve depicting utility level u 1 now as price has fallen the consumer now has made a tangency point between this budget line a B Prime with this indifference curve depicting utd level YouTube now as the price of quantity one has fallen further the new budget line has now created tangency with wait a minute now as the price consumption has to bend forward I had assumed that point of tangency beforehand so that I can easily draw the graph and now let us assume that at that selection point there is a tangency between the budget line ay B double prime and that denotes a utility level u3 so now note that these tangency points E 1 e 2 e 3 are all consumers equilibrium points depending upon the price of commodity 1 the consumer is facing so now to have the price consumption curve we know that we have to start from point A we need to move downwards first then we will draw an A with E and then we need to join e2 e2 e1 to e2 and then e2 to e3 and so on so forth so if we get a price consumption curve like that then this price consumption curve is downward-sloping and it is forward bending now let us see e under what circumstances this will be the case so let us look at the budget constraint again to have the answer so let us look at the budget constraint of the consumer so it is P 1 X 1 plus P 2 X 2 equals to M so M is the money income and P 1 X 1 plus P 2 X 2 is basically the expenditure on commodities 1 & 2 let us rewrite these as M minus P 1 X 1 over P 2 so as price of 1 Falls of course there will be an impact on X 1 commodity consumption for Goodwin and that's why this is going to be impacted depending upon how this impact is we get different levels of X 2 so depending upon the value or the behavior of P 1 X 1 with respect to price 1 change we see that X 2 can change so here in this case we see X 2 is continuously falling now ask x2 is continuously falling and x1 is continuously rising when is that possible if you look at the budget constraint equation you can see this is only possible when P 1 x1 is rising right so with a fall in price 1 if P 1 x1 is rising that means we are dealing with elastic demand function let me jot down these things for greater understanding so here P 1 is falling we see X 2 is continuously falling as a result that can only happen when P 1 X 1 is rising and that implies that we are observing a demand function for commodity 1 such that this is the own price elasticity mod value of that is higher than 1 so that means we are working with an elastic demand function for good one now let us move on to case number two in case number two we are going to study the case of first falling and then horizontal PCC so here we are not going to here we are not going to draw the individual indifference curves and budget lines to save time so I will straight away just you know draw the shape and then we are going to discuss so we are expecting something like this first falling and then it is becoming parallel to the X 1 axis now what does that mean that means that after some level of consumption the consumption of X 2 does not change anymore right so X 2 becomes constant so that means that from the budget equation P 1 X 1 becomes constant as well now if with a fall in P 1 P 1 X 1 becomes constant what does it imply it implies that the own price elasticity takes value 1 it implies that we are working with a demand function which shows unitary elasticity so let us jot down these things now we are going to study case number three and that is the case of u-shaped PCC so again we are going to have diagram X 1 and X 2 so if we are working with uShip then that means that price consumption curve first Falls it reaches a minimum and then it starts to rise again so this will be the PCC now when is that possible that means if we see this kind of shape that means that X 2 starts rising after some point as P 1 Falls now that can only happen if P 1 X 1 Falls as a result of fall in price of commodity 1 so what does that imply it implies that we are dealing with a demand function whose absolute value of own price elasticity is less than 1 so that means we are working with inelastic demand function for good one now we are going to look at the final case case for and in the case for we are going to talk about first falling and then the vertical price consumption curve so let us draw such a diagram so here we are talking about a PCC which first Falls and then after some point the consumption of commodity one does not change anymore with a fall in price of that commodity but consumption of comedy to keeps on rising and hence we get this kind of a shape now what does that mean x1 becomes constant the consumption of commodity one becomes constant as price falls now what does that mean it means that from the budget equation we observe P 1 X 1 does not change with a fall in P 1 so that means that we are working with the case of perfectly inelastic demand so although there is a fall in price the demand for commodity 1 does not change at all so we are working with elasticity value own price elasticity value equal to 0 for commodity 1 so let us note it down the result so now as we have seen four different shapes depending upon the values of own price elasticity let us also find some examples of commodities which fit well with these different cases so we are basically listing down some goods for which we can expect various values of on price elasticity so we are going to give you examples who is basically display the range of possibilities note that the goods that we are going to lease they are not the only examples you know there can be many many other goods but you know these are just for illustration purpose right so we are first going to talk about elastic demand so that means we are talking about this own price elasticity mod value of that takes value greater than one what would be the examples it can be a fruit like apple then there can be another example like these costly cars another example could be international air trips now we are going to give you some example of the other part which is in elastic demand so for that the mod value of one price elasticity is less than one what would be different examples the examples could be some commodities which we use on a daily basis like salt sugar milk then there could be clothing also because it is a necessity item for all of us then the third item would be electricity as example of inelastic demand now what would be an example of unit elastic demand it is very difficult to get such a real-life example it is also difficult to get example for perfectly inelastic demand the fourth case that we have seen but still there can be some examples for which you can think that elasticity value may be close to zero so let us you know take the example of some life-saving drugs once upon a time when insulin was the only medicine for diabetic patients insulin was the commodity for which the demand was perfectly inelastic so in the next lecture we are going to continue this discussion on the impact of price change on consumers equilibrium and demand next in the next lecture we are going to study what is known as price effect its decomposition via Slutsky equation [Music] [Music]