We should notice that the sum of the normalized

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Unformatted text preview: o w we get: PX = _4/19_ = _4_ w 1/19 1 PY = _6/19_ = _6_ w 1/19 1 r = _8/19_ = _8_ w 1/19 1 w = _1/19_ = _1_ w 1/19 1 resulting in the relative price vector (PX , PY , r , w)Rel. to L = (4 , 6 , 8 , 1). This works for all of the relative prices found using the numeraire method (shown in the table above). 93 So, as you can see, we can construct a lot of prices for a given set of four commodities! How many? Well, for a given set of four commodities (X , Y , K , L), we can have up to four sets of relative prices (one set for each choice of the numeraire) plus one set of normalized prices. In total, there are 4 commodities and 5 sets of prices (4 times 5 = 20) or 20 individual prices altogether. Does it matter if we change from one set of relative prices to another set of relative prices? That depends on the type of variables under consideration. Some economic variables change with prices while others do not. This is the distinction between nominal and real variables: [1] Nominal variables Nominal variables are variables which will change when we change from one set of relative prices to another. For example, if we increase or decrease prices, the following nominal variables will change accordingly: Endowment income Production Cost Profit [2] Real variables Real variables are variables which will not change when we change from one set of relative prices to another set of relative prices. For example, the following real variables will not change for the very simple reason that we divide both the numerator and denominator by the same number (i.e. the price of the numeraire): Demand for good X Demand for good Y MRS X = M / PX Y = M / PY MRS = Y / X K = C / r L = C / w MRTS = L / K 94 Me = PX X + PY Y C = rK + wL = PQ (rK + wL) Demand for Capital Demand for Labour MRTS The choice of the numeraire will also not affect the budget constraint equation: PXX + PYY = PX X + PY Y Which has prices PX and PY on both sides, it will not change if we divide both sides of the price of the numeraire. Consequently, the following consumer demand functions derived from the solution of the constrained ut...
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This note was uploaded on 05/25/2010 for the course ECON 301 taught by Professor Sning during the Spring '10 term at University of Warsaw.

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