Final Exam — Intermediate Macro (Sample, 2026) · worked-solution

• #macroeconomics
• #past-paper
• #worked-solution
• #development-accounting
• #production-function
• #labor-supply
• #gdp
• #inflation
• #investment
• #fiscal-policy
• #task-based-model

1. Q1 — TFP vs. capital in a growth-accounting comparison

   Two economies share the production function $Y = A K^{1/3} N^{2/3}$, population $1$, all employed ($N_1 = N_2 = 1$):

   Country	TFP ($A$)	Capital ($K$)	Labor ($N$)
   1	4	8,000	1
   2	2	1,000	1

   Economist A says capital explains most of the GDP gap (country 1 has $8\times$ the capital). Economist B says TFP differences contribute much more. Who is right?

   • 1
   • 2
   • 3
   • 4
2. Q2 — Immigration and the demand for robots

   Firms produce $Y = A K^{\alpha}[R + N]^{1-\alpha}$ with capital $K$ fixed in the short run, competitive wages, and a positive number of robots $R$. Immigration raises the supply of workers (new workers identical to residents); the price of robots is constant. Short-run effect on the demand for robots?

   • 1
   • 2
   • 3
   • 4
3. Q3 — Labor income tax with log-power utility

   Workers have $U(C,N) = \ln(C) - \theta\dfrac{N^{1+\psi}}{1+\psi}$ and budget constraint $C = (1-\tau_N)wN$ (labor income tax is the only tax). How does an increase in $\tau_N$ affect optimal labor supply?

   • 1
   • 2
   • 3
   • 4
4. Q4 — Emigration: GDP, GNP and NFP

   Ukrainian workers leave Ukraine (not replaced) and take jobs abroad at the same wage they earned at home. What happens to Ukrainian GDP, GNP and Net Factor Payments (NFP)?

   • 1
   • 2
   • 3
   • 4
5. Q5 — Unemployment rate from participation data

   Population $=5{,}000{,}000$; employed $=4{,}000{,}000$; not-employed $=1{,}000{,}000$; labor-force participation rate $=85\%$. The unemployment rate is:

   • 1
   • 2
   • 3
   • 4
6. Q6 — PCE deflator vs. CPI inflation

   A country produces oranges, bread and machines; 100 identical consumers consume only oranges and bread. Base year 2023.

   Year	Product	Qty	Price
   2023	Oranges	1,000	5
   2023	Bread	2,000	10
   2023	Machines	120	200
   2024	Oranges	1,100	6
   2024	Bread	1,500	15
   2024	Machines	125	180

   Find inflation from the PCE deflator and from the CPI (2023 basket).

   • 1
   • 2
   • 3
   • 4
7. Q7 — Backing out depreciation and investment from the investment rule

   Data: at $t$, $(N,K,Y)=(1000,100,100)$; at $t{+}1$, $(1050,105,120)$. Production $Y=A_tK_t^{0.3}N_t^{0.7}$; real rate $r=2\%$; capital tax $\tau_K=10\%$; price of capital constant at $10$. Capital at $t{+}1$ was chosen optimally (firms knew $A_{t+1}$). Find depreciation $\delta$ and investment $I_t$.

   • 1
   • 2
   • 3
   • 4
8. Q8 — Efficient labor allocation across firms

   Two firms, $Y_i = A_i K_i^{\alpha}N_i^{1-\alpha}$. Labor is fully mobile; capital is fixed at each firm with $K_1 > K_2$; TFP is equal, $A_1 = A_2$. In the efficient allocation:

   • 1
   • 2
   • 3
   • 4
9. Q9 — Liquidity constraints and the MPC across the income distribution

   The empirical findings discussed in class on liquidity constraints across the income distribution indicate that:

   • 1
   • 2
   • 3
   • 4
10. Q10 — PPP-adjusted GDP growth

    You measure Israel's PPP-adjusted GDP in current US dollars between $t$ and $t{+}1$. Assume: in Israel, inflation $=$ nominal-GDP growth; in the US, inflation was positive; GDP reflects the same basket in both countries. PPP-adjusted GDP in Israel:

    • 1
    • 2
    • 3
    • 4
11. Q11 — Two-period consumption with CRRA utility and the role of β

    Consumers live two periods with income $y_0, y_1 > 0$, no initial assets, utility $u(c_t) = \dfrac{c_t^{1-1/\sigma}}{1-1/\sigma}$ each period ($\sigma > 1$), discount factor $0<\beta<1$, real rate $r>0$. Which is correct?

    • 1
    • 2
    • 3
    • 4
12. Q12 — Forecasting the debt-to-GDP ratio

    Forecast next year's change in debt-to-GDP. Current ratio $b = 100\%$; planned primary deficit $d = 4\%$ of GDP; nominal rate $i = 5\%$; expected inflation $\pi^e = 3\%$. Also: 20 years ago real GDP $=10{,}000$, now $=18{,}000$, and future growth equals the 20-year average. Next year's ratio is about:

    • 1
    • 2
    • 3
    • 4
13. Q13 — GDP per capita vs. welfare

    The empirical findings discussed in class on GDP per capita vs. broader welfare / standard-of-living measures indicate that:

    • 1
    • 2
    • 3
    • 4
14. Q14 — Permanent TFP shock: investment vs. labor demand

    Production $Y_t = A_t K_t^{\alpha} + N_t^{1-\alpha}$ (note the additive form). Goods and labor markets in equilibrium. $A$ rises permanently. In the short run:

    • 1
    • 2
    • 3
    • 4
15. Q15 — Slope of the labor-supply curve with CRRA utility

    Workers have $U(C,N) = \dfrac{C^{1-\sigma}}{1-\sigma} - \theta\dfrac{N^{1+\psi}}{1+\psi}$ ($\sigma>0,\ \sigma\neq1,\ \theta,\psi>0$) with budget $C = wN$. Which is correct?

    • 1
    • 2
    • 3
    • 4
16. Q16 — Consumption tax financing a TFP-raising project

    Labor market in equilibrium; utility has no income/wealth effect on labor supply. Government raises the consumption tax $\tau_c$ and uses the proceeds on a productive project that raises TFP immediately and permanently. In the short run:

    • 1
    • 2
    • 3
    • 4
17. Q17 — Task-based model: productivity vs. displacement effects

    Task-based production $y(j) = \psi_N(j)N(j) + \psi_K(j)K(j)$; one unit of each task must be produced. $w=6$, $r=12$. Initial productivities:

    Task	$\psi_K(j)$	$\psi_N(j)$
    1	6	2
    2	4	3
    3	3	6

    Capital productivity in task 2 rises from $\psi_K(2)=4$ to $8$. Hold prices fixed first; supply curves upward-sloping; task allocation fixed after prices adjust. Which is correct?

    • 1
    • 2
    • 3
    • 4
18. Q18 — Interest-rate rise with log utility and only initial assets

    A consumer lives two periods, has initial assets $a>0$, no income ($y_0=y_1=0$), can borrow/save at $r>0$, discount factor $0<\beta<1$, and maximizes $\ln c_0 + \beta\ln c_1$. After choosing optimally, $r$ increases. As a result:

    • 1
    • 2
    • 3
    • 4
19. Q19 — Two claims: deflator/nominal-GDP and labor's share

    Claim 1: If the GDP deflator rises between two periods, nominal GDP grows faster than real GDP. Claim 2: If firms are competitive with $Y = AK^{\alpha}N^{1-\alpha}$ and hire labor optimally, labor's share of income is $(1-\alpha)$. Which is correct?

    • 1
    • 2
    • 3
    • 4
20. Q20 — Permanent capital-tax rise, proceeds rebated

    Standard consumption/labor/production/investment models; no income/wealth effect on labor supply. Government permanently raises the capital tax $\tau_K$ and rebates the proceeds lump-sum (net household income unchanged each period). "Short run" = before capital adjusts. As a result, in the short run:

    • 1
    • 2
    • 3
    • 4