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umn 6 by the absence of production shortages or surpluses. At output levels below $800 billion there is a shortage of output (aggregate spending is greater than production), while at output levels greater than $800 billion there is surplus production. The income-expenditure approach to output can be presented graphically beginning with the linear consumption function and the 45 line encountered in 4. Adding investment spending and net exports shifts the linear consumption function upward to the aggregate spending line (C + I + Xn). Aggregate spending equals output at only one level of output, determined by the intersection of the 45 line and the aggregate spending line. It can be shown that increases (upward shifts) or decreases (downward shifts) of aggregate spending increase or decrease the economy s equilibrium level of output. Example 5.1 The equilibrium level of output can be found algebraically by equating output and aggregate spending. Suppose the equation for the linear consumption function is C = $70 + 0.8Y; I is $120 and Xn = 0. Equilibrium output is found by solving Y = C + I + Xn for Y. Y = C + I + Xn Y = $70 + 0.8Y + $120 + 0 Y 0.8Y = $70 + $120 + 0 0.2Y = $190 Y = $190.2 = $950 datamatrix.net documentation . NET Data Matrix Generator for .NET, ASP.NET, C#, VB.NET
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Install our DataMatrix . NET Control and start Microsoft Visual Studio. Create a new project after that. Start Microsoft Visual Studio and create a new project. The leakage-injection model of equilibrium output focuses on saving and gross imports as leakages from the circular ow and on investment and gross exports as spending injections. Leakages depress aggregate spending, while injections increase aggregate spending. For example, spending on domestic output declines when individuals buy more imported rather than domestically produced commodities. An equilibrium level of output exists in the leakage-injection model when the sum of leakages equals the sum of injections. The distance determined in this manner is often referred to as the Euclidean distance in acknowledgment of its geometric origins, and the distance squared is known as the Euclidean distance metric. On this basis, the received codeword is closest to the 000 codeword, and the decoder would produce a binary 0 output. Soft decision decoding results in about a 2-dB reduction in the [Eb/N0] required for a given BER (Taub and Schilling, 1986). This reference also gives a table of comparative values for soft and hard decision coding for various block and convolutional codes. Clearly, soft decision decoding is more complex to implement than hard decision decoding and is only used where the improvement it provides must be had. 11.10 Shannon Capacity In a paper on the mathematical theory of communication (Shannon, 1948) Shannon showed that the probability of bit error could be made arbitrarily small by limiting the bit rate Rb to less than (and at most equal to) the channel capacity, denoted by C. Thus Rb C (11.17) For random noise where the spectrum density is flat (this is the N0 spectral density previously introduced) the channel capacity is given by C W log2 a1 S b N (11.18) Here, W is the baseband bandwidth, and S/N is the baseband signal to noise power ratio (not decibels). Shannon s theorem can be written as Rb W log2 a1 S b N (11.19) Letting PR represent the average signal power, and Tb the bit period then as shown by Eq. (10.17) the bit energy is Eb PRTb. The noise power is N WN0 and the signal to noise ratio is S N PR N Eb TbWN0 (11.20) The bit rate is Rb 1/Tb. Substituting this in Eq. (11.20) then in the inequality (11.19) gives Rb W log2 a1 R b Eb W N0 b (11.21) acScaleToFit ac1_128in_1ft ac1_64in_1ft ac1_32in_1ft ac1_16in_1ft ac3_32in_1ft ac1_8in_1ft ac3_16in_1ft ac1_4in_1ft ac3_8in_1ft ac1_2in_1ft ac3_4in_1ft ac1in_1ft ac3in_1ft As noted in Sec. 10.6.3, the ratio of bit rate to bandwidth (Rb/W in the inequality (11.21) is an important characteristic of any digital system. The greater this ratio, the more efficient the system. The limiting case is when the inequality sign is replaced by the equal sign. Rb W log2 a1 R b Eb W N0 b (11.22) vb net datamatrix 2d barcode DataMatrix . net - SourceForge
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