By David Romer
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Working backward, no one would ever want to sell goods for money and money would not be valued. 20 (a) (i) The individual has a utility function given by (1) U = lnC1,t + lnC2,t+1 , and a lifetime budget constraint given by (2) Qt C1,t + Qt+1 C2,t+1 = Qt (A - St ) + Qt+1 xSt . 18, we know that with log utility, the individual wants to consume A/2 in the first period. The way in which the individual accomplishes this depends on the gross rate of return on storage, x, relative to the gross rate of return on trading.
The equation describing the dynamics of the capital stock per unit of effective labor is now given by (2 ' ) k ( t ) f ( k ( t )) c( t ) G ( t ) ( n g) k ( t ) . The fact that the government is making purchases that do not add to the capital stock – it is assumed to be government consumption, not government investment – shifts down the k 0 locus. © 2012 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner.
The household would not want c to be low, and k thus marginal utility to be high, a moment before t1 knowing that c will jump up and be high, and thus marginal utility will be low, a moment after t1. The household would like to smooth consumption between the two instants in time. (d) We know that c cannot jump at time t1 . We also know that if the economy is to reach the new balanced growth path at point ENEW , it must be right on the new saddle path at the time that the tax is put in place. Thus when the tax is announced at time t0 , c must jump up to a point such as A.