Question

What is the mathematical condition prevailing when the consumer sets its optimum combination of (two) goods he/she consumes. What is the adjustment process if this condition does not prevail? Why would there be utility gain as the individual moves toward the optimum—w/o spending more of his/her income.

Answer 1

X2 suppose the consten Spuds all of his / her in come on two goods x, and Xr. where in come & = M, Price of XI = Pxi and Price of X2 = Px2, Hence his/hen budget constraint - Ma Pixit bz Xz Now slope of this budget constraints PX2 Now, we know that utility fiction of this consum - U= u(X1, X2) -Swhere ned Slope of this in dit scance emul is to the CamScanner

one good with other o rate at which consues substitutes one good with - good to This slope is the marginal rate of subst the (MRS) etwan two goods or betwan Xl and X₂ je MRSX 1/2 Now the targuicy condition requires that, at optimal utility level, slope of indiffunce (muc= slope of budget lie. or MRSX1 X2 = PxH PX2 where MRS X) X2 = I and mux, = Marginal R MUX2 stility of Xi and MUX2 = Marginal utility of X2 . This happes at point in in the figme and optimal combinations of two goods are & (x* X22 ). Now when the tangency condition ý not satisfied say, at point n, where an indiftunce couc cuts the dont line, then the slope of Indiblunce care or ac is lown than the price rato. Hace consuees can do better by buying less of good 1 and more good 2. because it she buys less of good 1, then Mux, will inneare and it she bys more of Gooda, then MUX2 will fall to mux will rise lie slope of indistance love will risc and eventually will become equal to the slope of budget line or equal to the pure ratio Px, Pxz' Arte, Fue Hace, it the targency condition is not satis find then, the rate at which good 1 and goodz are traded (MRS XX2) becomes different that the rate at which they are traded in a hanket (PAL) and utility will not be smaninama budgit li tice the ratio muxi will МО