Microeconomics: Relationship between the income and substitution effects and how they changes under different circumstances.
In this essay I will consider about the relationship between the income and substitution effects and how they changes under different circumstances. As definition, the substitution effect is ‘‘the effect of a price change on the quantity demanded due exclusively to the fact that its relative price has changed“ (Morgan, Katz and Rosen, p.106, 2006 ) and the income effect is ‘‘the effect of a price change on the quantity demanded due exclusively to the fact that the consumer‘s real income has changed“ (Morgan, Katz and Rosen, p.106, 2006 ).
This essay is dedicated to answer the question :‘‘ What about the situation for a net borrower when the interest rate falls: what is the relationship between the income and substitution effects on the optimal choice of current consumption? “ In this case, the substitution and income effect coincide and even reinforce each other - both of them cause the current consumption growth. This is because if the interest rate falls, the borrower increase its consumption, because (as he borrows) he has to pay less money to his creditors, so it makes he feel richer. So relatively his incomes growth. So, as the current consumption is the normal good, the income increase causes growth of consuming.
Another solution of this model is that as the opportunity cost of current consumption decreases because of the reduction of the amount of future consumption ( because interest rates have felt). This tends to increase current consumption what means to borrow more, because it becomes relatively cheaper than save it to the future consumption.
For saver, the reduce in the interest rate can cause opposite result. The substitution effect leads that the saver will save less because of that the opportunity cost of current consumption has decreased in case to the future consumption, so it is makes more utility to increase current consumption.
The income effect claims conversely. As the income rate falls, the saver will save more, because he fells poorer as the people whom he borrowed money give him less amount than previously, because of the interest rate falling. So as the consumption is normal good, it‘s consuming will decrease and tha saver will save more.
If the interest rate rise, the consequences for saver also can be contrary. It depends on the situation of the saver. If he or she is a ‘‘target saver “ when the interest rate growth will lead to the decrease in saving. This is because of that the saver has in his goal the exactly amount of sum, which he has to save and so the interest rate growth or fall leads to the totally different result.
Take into account the another model - household labour supply. As the wages increase in the income-leisure trade-off graphic, the leisure consumption tends to be controversial. The substitution effect leads to the assumption that a person will work more as the opportunity cost of hour of leisure has grown. In other case, the income effect sais that, as the wage rate has grown , the incomes have also increased, so there is no point to work as much as previously if it is posible to gain the same amount of income and have the same level of utility by working less and having more leisure.
Graph 1. Substitution and income effect : A Decrease in Interest Rate Increases Borrowing
In this graph, individual‘s endowment point is E (when he consumes Iº in the present and I¹ in the future), but as he is a borrower, his utility maximation point is A (when he consumes Cº in the present and C¹ in the future ),where budget constraint is the tangent to the individual's indifference curve. At this point he borrows amount Cº - Iº, with the interest rate i. And his future consumption decrease by the amount of money I¹ - C¹.
As the interest rate falls ( from i to i¹ ), we draw new inter-temporal budget constraint from B¹ to B². This new constraint must also pass through the endowment point because individual always has the option of neither borrowing, nor lending. So it also pass through the point E. Though new budget constraint is flatter because the opportunity cost on one money equivalent (suppose euro) of current consumption is only I+ i¹ euros of future consumption.
Subject to constraint B², borrower maximizes his utility at the point B, where he consumes Cº´ in the present and C¹´ in the future. Because of the decline in interest rate, his borrowing growth from Cº - Iº to Cº´ - Iº. This is because of the substitution effect which sais that opportunity cost of current consumption decreases because of the reduction in amount of future consumption which is tied with each euro of current consumption. So this tends to increase current consumption, and therefore decrease saving. The substitution effect here is Cº´ - Cº.
The income effect also tends to increase current consumption.
Graph 2. Substitution and Income Effect : The Decrease in the Interest Rate Lowers Saving
In this case the substitution has the same effect on the optimal choice of current consumption for saver when the interest rate changes ( suppose, fell) as in the situation for borrower when interest rate also fells. In both cases substitution effect leads to increase current consumption, what for saver means to reduce saving and for borrower means to increase borrowing, because as the interest rate falls, the opportunity cost of current consumption decreased.
However, in these two situations the income effect has opposite results. For saver the interest rate decreasing leads to lower current consumption and increase saving. For borrower it is contrary. The income effect tends to increase current consumption, because as the interest rate falls, borrower relatively feels richer, as he has to pay less for his creditors. As current consumption is a normal good, so having more income borrower consumes more of it.
Graph 3. The Substitution and Income Effect : An Increase in Wages Increases the Labour Supplied
File:Labour supply income and substitution effects small.png
In this case, analysing household labour supply, based on the income-leisure trade-off, when wage rate increase, the substitution and income effect in leisure are opposed one another.
In the graph above, Y¹ line shows original budget constraint and line Y² shows the budget constraint after the increase in wage. A is the point where the utility is maximized, when X- XA hours of work are supplied to the market and the consumption level is YA. After the increase in wages, the new utility's maximization point is B, where X - Xb hours of work is supplied and Yb level of consumption is reached.
To find substitution effect of a wage increase, the budget constraint Y¹ is shifted up until it is tangent to the new indifference curve, at point C. The substitution effect is the movement from point C to point B. This is because as the wage rate rises, the worker will substitute work hours for leisure hours, that is, will work more hours to take advantage of the higher wage rate, or in other words substitute away from leisure because it has a higher opportunity cost.
The income effect in this graph is shown as the movement from point A to point C. Consumption increases from YA to YC and assuming leisure is a normal good, leisure time increases from XA to XC (so work time decreases by the same amount; XA to XC).
The net impact of these two effects is shown by the shift from point A to point B. The substitution effect dominates the income effect; hence, in this case the growth in wage rate increases the supply of labour. But the relative magnitude of the two effects depends on the circumstances. In some cases the substitution effect is greater than the income effect (in which case more time will be allocated to working), but in other cases the income effect will be greater than the substitution effect (in which case less time is allocated to working).
In this essay I have considered the relationship of substitution and income effect and made a solution that these effects relationship depends on several aspects - the individual preferences and the quality of good ( is it a normal or not ).
Wyn Morgan, Michael Katz & Harvey Rosen “Microeconomics” (2006)