Lecture # 11 -- Applicatins f Utility Maximizatin/Prductin I. Examples: Incme and Substitutin Effects As an example f substitutin and incme effects, we lked at research n child labr and rice farms in Vietnam, based n the New Yrk Times article n the syllabus. Mst child labr in develping cuntries is in agriculture. Recent research suggests that child labr is related t pverty. As incmes increase, mre children g t schl. This relates t the pprtunity cst f sending children t schl. The pprtunity cst f sending a child t schl is that the prductivity f this child n the farm is lst. This is mre valuable t lw-incme families. Because f diminishing marginal utility, the extra incme a lw-incme family gets is mre imprtant t them than it wuld be t a family with higher incme. Mrever, families with higher incmes can affrd substitutes fr child labr, such as fertilizer r tractrs. The article applies this t rice farms in Vietnam after Vietnam repealed a law prhibiting the exprt f rice. Repealing the ban n exprts increased the ptential market fr rice, thus raising its value. As a result, the pprtunity cst f sending a child t schl increased fr families that grw rice. Nnetheless, after the plicy tk effect, researchers fund that mre f these children went t schl. The level f child labr n rice farms fell! The explanatin cmes frm substitutin and incme effects. It is true that the substitutin effect means that farmers will want t use mre child labr, since it is nw mre valuable. Hwever, the incme effect enables mre farmers t send their children t schl. In this case, the substitutin and incme effects g in ppsite directins. Here, the incme effect dminated, s child labr decreased, and the number f children attending schl increased.
In the graph belw, a family chses sending a child t schl (educatin) r earning incme frm their wrk n the farm. The family starts at pint A. By raising the pprtunity cst f ging t schl, repealing the exprt ban causes the budget line t rtate. The new cnstraint is the red line belw. Nte that it pivts alng the x-axis. There is n mre time t g t schl, s the maximum level f educatin is the same. Hwever, if children stay at hme t wrk, they generate mre incme. The final change ges frm A t B. Bth educatin and ther incme increase. If we tk away the extra incme that farmers earned, families wuld face the blue budget line. This returns their utility t the riginal level, but represents the new higher pprtunity cst f ging t schl. Thus, the substitutin effect (A t C) des cause schling t decrease. Hwever, the incme effect (C t B) ges in the ppsite directin, and is s strng that schling increases despite the higher pprtunity cst.
Our secnd example illustrates the results f a recent study n fd subsidies. The study tested a pilt prgram where families were given subsidies t purchase healthy fds. Fr high incme families, the share f healthy fd in their diet increased. Hwever, fr lw incme families, the share f healthy fd decreased. Instead, they used their extra incme t purchase mre f the fds they liked best, even if they weren t healthy. Thus, the incme effect dminated the substitutin effect. The graph belw illustrates. Here, a family chses between healthy fd and ther fd. The family starts at pint A. The subsidy lwers the cst f healthy fd. The budget cnstraint rtates ut, as shwn by the red line belw. The ttal change in cnsumptin ges frm A t B. Cnsumptin f bth types f fd increases, but there is a larger increase in nn-healthy fd. If we tk away the extra incme prvided by the subsidies, families wuld face the blue budget line. This returns their utility t the riginal level, but represents the new lwer cst f healthy fd. Thus, the substitutin effect (A t C) des cause families t chse mre healthy fd. Hwever, the incme effect (C t B) causes families ges in the ppsite directin. Families use their extra purchasing pwer t purchase mre f the types f fd they like best. The key pint f this example is that the incme effect culd wrk against the intended effect f yur plicy. Thus, it is imprtant t understand what the incme effect might be, and if it wrks against yu, hw big it might be.
II. Behaviral Ecnmics Behaviral ecnmics cmbines psychlgy and ecnmics, and ntes cases where bserved behavir differs frm what traditinal ecnmic mdels predict Systematic biases create a difference between decisin utility and experienced utility. Decisin utility is the utility cnsumers maximize at the time f chice Experienced utility is the utility cnsumers later realize as a result f a prir decisin Behaviral anmalies that lead t a difference between decisin utility and experienced utility are behaviral failures Behaviral ecnmics prvides examples where peple make predictable errrs, rather than just randm errrs. Nte that if preferences are nt stable ver time, using cnsumer decisins t infer utility will lead t incrrect predictins. This led t ur discussin f the rle that plicy culd play t help crrect the bias in actual decisins.
III. Prductin Functins Where we are ging: Our gal in the next 3 weeks is t derive the supply curve. There are three steps: 1. Define prductin 2. Cst minimizatin What is the cheapest way t prduce a given level f utput? 3. Prfit maximizatin Given cst minimizatin, hw much shuld we prduce? We begin by using prductin functins t describe the prductin prcess. Firms take inputs and transfrm them int utputs. A prductin functin describes this prcess. Prductin functin -- indicates the maximum amunt f utput that can be btained fr any cmbinatin f inputs with a given technlgy. Nte that changes in technlgy change the prductin functin. Describes what is technically feasible when the firm perates efficiently. IV. The Shrt-Run: Prductin With Fixed and Variable Inputs Shrt run -- A perid f time s brief that at least ne factr f prductin is fixed, and cannt be changed Fixed inputs are inputs such as machinery and factries that take time t change. In general, we will classify the fixed inputs as capital (K). Lng run -- A perid f time lng enugh s that all inputs can be varied. Fr nw, we hld capital cnstant, and lk at what happens as we vary labr. We begin with three definitins: Ttal prduct f labr (TPL) -- Shws what happens t utput when the firm changes ne f its inputs, hlding all thers cnstant. Marginal prduct f labr (MPL) -- Additinal utput resulting frm a neunit increase in labr, hlding all ther inputs cnstant. (MPL = change in q/change in L) Average prduct f labr (APL) -- Output per unit f labr. (APL = q/l)