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Brief answers to Problems for the class on Feb 21
Ch.3: problem 7 (p.77)
a. Public saving = T –G. Because △T=$100 billion & △G=$0 Public saving rises by the full amount, $100 billion.
b. Private saving = (Y-T)-C. Because Y is fixed and not affected by the change in taxes, Δ(Y-T) = -ΔT=-$100 billion (a decrease) Consumption falls by MPC∗Δ(Y-T) = 0.6 ∗$100 billion=$60 billion, and saving falls by (1-MPC)∗Δ(Y-T)=0.4∗$100 billion=$40 billion.
c. National saving = Public saving + Private saving The change in national saving = the sum of the changes in public and private saving = $100 billion - $40 billion = $60 billion (an increase). d. Investment equals saving in equilibrium, so investment must rise by $60 billion.
Ch.4: problem 4 (p.114-115)
Money market equilibrium condition (M/P)d = (M/P)s = M/P M/P = kY. Convert this to the percentange-change relationship to and arrange to have
ΔP/P + ΔY/Y = ΔM/M + ΔV/V (i)
with V=1/k
a. When k is constant, so is V. (i) the (average) inflation rate ΔP/P = ΔM/M + ΔV/V -ΔY/Y = 12% + 0% - 4% = 8%.
b. From (i), ΔY/Y↑ ΔP/P↓, i.e. if real income growth were higher, then real money demand would grow faster and inflation would be lower.
c. From (i), if ΔY/Y and ΔM/M remain the same, then ΔV/V↑ ΔP/P↑. In words, if the velocity of money were growing steadily, then real money demand would grow less rapidly than real income. For a given growth rate of the money supply, inflation would therefore be higher than when velocity is constant.
Ch.6: problem 3 (p.188)
Define terms as follows, I: # of involved people (call this the I pool), U: # of uninvolved people (call this the U pool), b: the rate of breakup, r: the rate of entering a relationship. Because among involved people, 10% experience a breakup of their relationship every month, the rate of breakup is b=10%. Similarly, r=5%. People experiencing a breakup will move from the I pool to the U pool, so the # of people moving from I to U = the # of people experiencing a breakup = bI. Similarly, the # of people moving from U to I = the # of people newly having a relationship = rU. In the steady-state, these two flows must be equal, so bI= rU I = rU/b =(r/b)/U the total # of people in the dorm U+I = U + (r/b)/U = [(b+r)/b]/U the fraction of residents who are uninvolved = U/(U+I) = U/{[(b+r)/b]/U} = b/(b+r) = 10%/(10%+5%) = 2/3.
2 Ch.9: problem 2 (p.285)
a. The aggregate demand curve will shift to the left (draw the graph to confirm this).
b. In the short run, the price level is fixed, so the level of output will decline. In the long run, the price level will decline and output will return to its natural or fullemployment level.
c. According to Okun’s law, output and unemployment are negatively correlated. Therefore, following b., in the short run when output falls short of its full-employment level, the actual unemployment rate will rise above the natural rate of unemployment. In the long run, output will return to its natural level, the actual unemployment rate will return to its natural level as well. d. In the short run, the decline in the level of output will reduce saving and lead to a rise in the real
interest rate in order for investment to decline and equal the lower level of saving. In the long run, output will return to its full-employment level and the real interest rate will decline to its original value.
Ch.11: problem 2 (p.336)
a. When many firms decide to upgrade their computer system, they increase their investment I↑ the IS curve shift to the right Y↑, C↑, r↑ (note from the consumption function that Y↑ C↑). The central bank’s response to keep Y unchanged: reduces money supply, shifting the LM curve to the left (draw the graph to confirm this).
b. A wave of credit-card fraud increases the frequency with which people make transactions in cash real money demand↑ the LM curve shift to the left Y↓, C↓, r↑. The central bank’s response to keep Y unchanged: increases money supply, shifting the LM curve back to the right (draw the graph to confirm this).
c. A best-seller titled Retire Rich convinces the public to increase the percentage of their income devoted to saving MPC↓ the IS curve becomes steeper Y↓, C↓, r↓. The central bank’s response to keep Y unchanged: increases money supply, shifting the LM curve to the right (draw the graph to confirm this).
Ch.13: problem 1 (p.402)
The equation of the AS curve obtained in the sticky-price model P = EP + [(1-s)a/s](Y-Y*) (ii)
(Y* is the natural rate of output and corresponds to Y_bar in the textbook.)
a. When no firms have flexible prices, it means that all firms have fixed (or sticky) prices. In this case, s=1 or 1-s=0, and thus (ii) becomes P = EP = P0, where P0 is the level to which prices are fixed (the second equality holds because all firms have fixed prices (P0) so the expected value of the price level is also fixed at P0). Thus, P = P0 is the equation of AS curve in this case, and it
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implies a horizontal AS curve. This is also the SRAS curve discussed in Ch. 9.
b. When the desired price does not depend on aggregate output, or a=0, it means that firms do not respond to the gap between actual and natural output, and they set their prices based only on the expected value of the price level. In this case we also have a horizontal AS curve, as seen in (ii). The difference between the SRAS curve discussed in Ch. 9 is the presence of EP which did not appear in the Ch. 9.
