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Unformatted text preview: tors (X , Y , K , L) as a unit of value (called a numeraire) and express the prices of the remaining goods and factors in terms of this unit of value. These prices, when expressed in terms of this unit of value, are called the relative prices. So, a numeraire is an archaic French term originally used by Walras to refer to the good or factor which has been selected as the unit of value. Once a good or factor has been selected as a numeraire, the prices of all other goods and factors are expressed in terms of their relative value to the numeraire. The numeraire itself is simply the good or factor that has a relative price (its price relative to its own price) equal to one. How do you choose and calculate the numeraire? We can illustrate this process quite easily. Since the numeraire is just an arbitrary designation; any good or factor can be a numeraire. Consider the price vector (PX , PY , r , w) = (2 , 3 , 4 , )... Good / Factor Selected to be the Numeraire GOOD X (divide all by PX = 2) GOOD Y (divide all by PY = 3) CAPITAL (divide all by r = 4) LABOUR (divide all by w = ) GOOD X PX = 2 1 2/3 4 GOOD Y PY = 3 3/2 1 6 CAPITAL LABOUR r=4 w= 2 4/3 1/6 1 1/8 8 1 Now, of course, this is not the only way to get relative prices... Instead of choosing a numeraire and dividing all the remaining prices by the price of the numeraire good / factor, we can get normalized relative prices in the following two steps:  First, we need to get the sum of all the prices: = 2 + 3 + 4 + = 19/2  Then we divide all prices by this sum 92 PX = _2_ = _4_ 19 PY = _3_ = _6_ 19 r = _4_ = _8_ 19 w = _1/2_ = _1_ 19 This process of dividing all prices by the sum is called normalization and the prices calculated are called normalized prices. We should notice that the sum of the normalized prices is equal to one. PX + PY + r + w = 4/19 + 6/19 + 8/19 + 1/19 = 19/19 =1 The reason for this is simply that we have divided all prices by (which is the sum of all prices). Now, notice that we can obtain the relative prices that we calculated in the chart before by taking the ratios of the normalized prices. For example, when we used labour as the numeraire we had the relative price vector (PX , PY , r , w)Rel. to L = (4 , 6 , 8 , 1) and if we use normalized prices and take their ratio t...
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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.
- Spring '10