Lecture # 9 -- Cnsumer Behavir: Maximizing Utility I. Marginal Rate f Substitutin Marginal Rate f Substitutin (MRS) is the rate at which a persn will give up gd y in rder t get mre f gd x and still have the same utility. It is equal t the negative f the slpe f the indifference curve In the example belw, as we mve frm pint A t pint B, we give up 2 units f Y t gain ne unit f X. Thus, the slpe f the indifference curve in this regin is -2, and the MRS = 2. As we mve alng the indifference curve, the curve gets flatter, and the MRS is lwer. Mving frm C t D, we are nly willing t give up 0.5 units f Y t get ne unit f X. Thus, the slpe f the indifference curve in this regin is -0.5, and the MRS = 0.5.
MRS = MUX/MUY Thus, MRS tells us the rati f the marginal utilities. Nte that, as we mve alng the indifference curve, the MRS gets lwer. Frm A t B, where the MRS = 2, X is mre valuable than Y, since we have mre Y than X. Here, as a result, the marginal utility f X is twice that f Y. Frm C t D, where the MRS = 0.5, Y is mre valuable than X. The marginal utility f X is just half that f Y. This result fllws frm diminishing returns. When we have mre f X, we place less imprtance n getting even mre. II. The Budget Cnstraint Nw that we have a way f describing preferences, we need t intrduce a cnstraint. The cnstraint will be the incme that the cnsumer has available t spend. The Budget Cnstraint is all pssible cmbinatins f tw cmmdities that are affrdable, given prices and a fixed amunt f incme. I = PxX + PyY
The intercepts represent the amunt f the gd yu can get if yu spend all yur incme n that gd (I/Px and I/Py). Changes in incme lead t parallel shifts f the budget cnstraint. The slpe (-Px/Py) represents the relative prices. It tells hw much f Y yu need t give up t affrd anther unit f X. Changes in prices cause the line t rtate. In the example belw, Px1 is lwer than Px0. Thus, we can affrd mre, s the budget cnstraint rtates utward. Nte in general that fcusing n hw bundles n the rigin change (e.g. if yu spend all f yur mney n nly ne gd) can help determine hw t change the budget cnstraint as incme r prices change.
Next, we illustrated examples f budget cnstraints with unusual shapes. Bulk discunts When prices vary as quantity varies, the budget cnstraint will have sectins with different slpes. Example: PX = $1 fr the first 100 units, and $0.50 thereafter. Incme = $200. Key pints: Hw much ther cnsumptin is pssible if n X is purchased? ($200 wrth). What is the maximum amunt f X that can be purchased? If 100 is purchased at $1 each, yu have $100 remaining. Since the remaining units nw cst $0.50, up t 200 units may be purchased with the last $100. Thus, a maximum f 300 units f X may be purchased. Where des the slpe f the budget cnstraint change? The slpe changes where the prices change. This ccurs where X = 100. At this pint, there is $100 fr ther cnsumptin.
III. Which Bundle t Chse? Maximizing Utility What must be true abut the maximizing bundle? 1. It must be n the budget cnstraint. 2. It must be n the highest pssible indifference curve. When this ccurs, the indifference curve and budget cnstraint will be tangent. MRS = MUx/MUy = Px/Py, r: MUx/Px = MUy/Py The marginal utility per dllar spent n x equals the marginal utility spent per dllar n y. If nt, utility culd be imprved by spending less n the gd with a lwer marginal utility per dllar and mre n the gd with a higher marginal utility per dllar. Nte the imprtance f marginal analysis. In general, things are maximized when they are equal at the margin.
IV. In Kind Transfers In-kind transfers In-kind transfers are when aid is given as a cmmdity, rather than in cash, such as fd stamps In the example belw, I use a $5000 educatin vucher as an example f an in-kind transfer. The vuchers are like an increase in incme. Thus, the budget cnstraint shifts ut. Nte that prices remain the same, s the slpe must remain the same. Hwever, the budget cnstraint is cut ff at the tp, since sme incme will be spent n educatin. It is nt pssible t spend $5000 mre n ther cnsumptin and $0 n educatin. In general, nte that the key fr graphing budget cnstraints is finding the relevant end pints.
In kind transfers, in which aid is given as a cmmdity, rather than cash, may lead t crner slutins When we are at a crner slutin, marginal utility per dllar is nt equal, s cnsumers are being hurt by a cnstraint. In the vucher example, the cnsumer wuld have preferred t spend less n educatin than the amunt allcated in vuchers, but cannt. The persn is maximizing utility given the additinal cnstraint f the vucher prgram, but wuld even be happier if cash was given instead. This is shwn in the graph belw. Nte that, had we given this family cash instead (represented by the dashed line), they culd have attained higher utility, represented by the red indifference curve. Mrever, as the article n aid in India discusses, in kind transfers may lead t ther prblems, such as a black market develping. Hwever, such plicies d ensure that the aid is used as the dnr intended.