26  Full exam — 30 questions, timed

Aim for 60 minutes. Write down your answers before checking. Solutions are at the end.

26.1 Section 1: CPI, unemployment (5 questions)

1. Basket = 8 units of food, 5 units of computers. 2019 prices: food $5, computers $10. 2021 prices: food $7, computers $12. Base year = 2019. Find CPI in 2021 and inflation 2019→2021.

2. CPI in 2020 = 110, CPI in 2024 = 132. Find inflation 2020→2024.

3. Labor force = 160 million. Employed = 152 million. Find unemployment rate.

4. A factory closes; 1,000 workers lose their jobs. 800 start looking for new jobs. 200 give up and stop looking. By how much do (a) U, (b) LF, (c) u change?

5. Frictional, structural, cyclical, natural rate — define each in one sentence.

26.2 Section 2: Equilibrium income (6 questions)

6. C = 50 + 0.80Y, \overline{I} = 30. Find Y^* and the multiplier.

7. Same setup. \overline{I} rises to 50. Find new Y^*.

8. \overline{C_0} = 80, c = 0.75, \overline{T} = 40, \overline{I} = 50, \overline{G} = 100, \overline{X} = 60, \overline{M} = 30. Find Y^*.

9. Same as Q8. Imports rise to \overline{M} = 60 (e.g., new free-trade deal). Find new Y^*.

10. Y^* = 1{,}000. \overline{C_0} = 200, \overline{I} = 50. Find MPC.

11. MPS = 0.40. Y^* falls by 80. The Treasury blames falling \overline{I}. By how much did \overline{I} fall?

26.3 Section 3: Fiscal policy (4 questions)

12. Y^* = 8{,}000, Y^{FE} = 8{,}500. MPC = 0.80. Close the gap with \overline{G} alone.

13. Same setup. Close it with \overline{T} alone.

14. Same setup. Close it with the balanced-budget combination.

15. Same setup. The Treasury raises \overline{G} by 50 and raises \overline{T} by 100. By how much does Y^* change?

26.4 Section 4: Money & banking (4 questions)

16. rrr = 15\%. Find K_S.

17. Fed buys $200 in bonds. rrr = 10\%. Find \Delta M^S.

18. Bank: TR = 50, DD_p = 200, rrr = 0.20. Compute RR, ER, and the maximum new loans this single bank can extend.

19. Fed cuts rrr from 20% to 10%. Banking system has DD_p = \$1{,}000 and was previously fully loaned up. By how much can M^S now expand?

26.5 Section 5: Money market and bonds (4 questions)

20. A 5-year bond has FV = \$1{,}000 and r = 4\%. Find PV.

21. A 10-year bond has FV = \$1{,}000 and trades at $600. Find implied r.

22. r > r^* (excess supply of money). Bond prices and r both move toward equilibrium. In which direction does each move?

23. Fed buys bonds. Trace the chain: M^S, bond prices, r^*, I^d, Y^*.

26.6 Section 6: Open economy (4 questions)

24. US basket costs $400. UK basket costs £200. Find PPP E_{\$/£}.

25. US inflation = 5%/year, UK = 2%. PPP rate today is $2.00/£. Project the rate in 3 years.

26. US interest rate falls relative to UK. Direction of \$ vs. £?

27. US dollar depreciates 10%. Trace effect on EX, IM, (X-M), Y^*, P.

26.7 Section 7: Synthesis (3 questions)

28. Fed conducts an OMO purchase under FLOATING exchange rates. Trace through both channels (interest-rate and FX). What’s the net effect on Y?

29. Same OMO under FIXED exchange rates. Why is the net effect on Y much smaller?

30. What is the trilemma and what does it imply about a country that wants to join a currency union?

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26.8 Solutions

1. Cost of base basket at 2019 prices: 8(5) + 5(10) = 90. CPI(2019) = 100. Cost at 2021 prices: 8(7) + 5(12) = 116. CPI(2021) = 116/90 \cdot 100 = 128.89. Inflation = $(128.89 - 100)/100 = $ 28.89%.

2. $(132-110)/110 = $ 20%.

3. u = U/(E+U). U = 160-152 = 8. $u = 8/160 = $ 5%.

4. (a) U rises by 800 (those still looking). (b) LF falls by 200 (the discouraged ones leave). (c) u rises (numerator up by 800, denominator down by 200).

5. Frictional: short-run job/skill matching. Structural: industry-level decline; permanent skill mismatch. Cyclical: recession-driven, disappears in expansion. Natural rate: frictional + structural; ~4%.

6. K = 1/(1-0.80) = 5. $Y^* = (50+30)/0.20 = $ 400. Multiplier = 5.

7. \Delta\overline{I} = 20. \Delta Y^* = 5 \cdot 20 = 100. New $Y^* = $ 500.

8. K_G = 1/0.25 = 4. K_T = -0.75/0.25 = -3. $Y^* = 4 (80 + 50 + 100 + 60 - 30) - 3 = 4 - 120 = 1040 - 120 = $ 920.

9. \Delta\overline{M} = +30. K_{IM} = -4. \Delta Y^* = -4 \cdot 30 = -120. New $Y^* = $ 800.

10. 1-c = (200+50)/1000 = 0.25. So $c = $ 0.75.

11. K_I = 1/0.40 = 2.5. $ = -80/2.5 = $ −32.

12. Gap = 500. K_G = 5. $ = 500/5 = $ 100.

13. K_T = -4. $ = 500/(-4) = $ −125 (cut taxes by 125).

14. K_{BB} = 1. $ = = $ 500.

15. $Y^* = 50 + 100 (-4) = 250 - 400 = $ −150. The economy contracts because the tax hike outweighs the spending boost.

16. $K_S = 1/0.15 = $ 6.67.

17. K_S = 1/0.10 = 10. $M^S = 10 = $ $2,000.

18. RR = 0.20 \cdot 200 = 40. $ER = 50 - 40 = $ 10. The bank can extend up to $10 in new loans.

19. Old: RR = 0.20 \cdot 1000 = 200, ER = 0. New: RR = 0.10 \cdot 1000 = 100, so freed ER = 100. New K_S = 10. Expansion = $10 = $ $1,000.

20. $PV = 1000/1.04^5 = 1000/1.2167 = $ $821.93.

21. $r = (1000/600)^{1/10} - 1 = 1.6667^{0.1} - 1 - 1 = $ 5.24%.

22. r falls (toward r^*). Bond prices rise.

23. OMO purchase: \Delta R > 0 \Rightarrow \uparrow M^S \Rightarrow bond prices rise \Rightarrow r^* falls \Rightarrow I^d rises \Rightarrow Y^* rises.

24. $E_{$/£} = 400/200 = $ $2.00/£.

25. US prices in 3 years: 400 \cdot 1.05^3 = 463.05. UK: 200 \cdot 1.02^3 = 212.24. PPP: $463.05/212.24 = $ $2.18/£ ($ depreciated).

26. Lower US rate relative to UK \Rightarrow capital flows from US to UK \Rightarrow supply of \$ rises, demand for £ rises \Rightarrow $ depreciates, £ appreciates.

27. \uparrow EX (US goods cheaper abroad). \downarrow IM (foreign goods more expensive in US). (X-M) rises. AE^d shifts up. Y^* rises. P also rises (AD shifts right).

28. Channel 1: \uparrow M^S \Rightarrow \downarrow r \Rightarrow \uparrow I^d \Rightarrow \uparrow Y. Channel 2: \downarrow r \Rightarrow capital outflow \Rightarrow \$ depreciates \Rightarrow \uparrow (X-M) \Rightarrow \uparrow Y. Both push Y up. Monetary policy is potent.

29. Channel 2 is dead — the central bank must intervene to keep ER stable, contracting M^S back. Only channel 1 operates, partially. Net effect on Y is muted.

30. Trilemma: a country can have at most two of {free capital flow, fixed ER, independent monetary policy}. Joining a currency union is choosing free capital + fixed ER (effectively, sharing a currency = ultimate fix). The country gives up independent monetary policy — the central bank for the union sets policy for the whole bloc.

26.9 Score yourself

out of 30	what to do
27–30	Done. Sleep.
22–26	Re-do the wrong ones from the chapter, not from memory.
16–21	Read the chapters that cover your weakest section.
≤ 15	Need a serious study session. Start with the formula card and the decision tree.