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2026 PEA Q29

Two Solow economies A,BA, B share the same technology and n=0.02n = 0.02. They have kA=3,kA∗=9k_A = 3, k^*_A = 9 and kB=4,kB∗=16k_B = 4, k^*_B = 16. Then per capita output is growing

Reveal answer and solution

Answer

B

Solution

  1. 1

    As in Question 28, si=n (ki∗)1/2s_i = n\,(k^*_i)^{1/2}. Thus sA=0.02⋅3=0.06s_A = 0.02\cdot 3 = 0.06 and

  2. 2

    sB=0.02⋅4=0.08s_B = 0.02\cdot 4 = 0.08. The current growth rate of capital per worker is

  3. 3

    k˙i/ki=si/ki−n\dot k_i/k_i = s_i/\sqrt{k_i} - n, so

  4. 4
    k˙AkA=0.063−0.02≈0.0346−0.02=0.0146,k˙BkB=0.082−0.02=0.04−0.02=0.02. \frac{\dot k_A}{k_A} = \frac{0.06}{\sqrt 3} - 0.02 \approx 0.0346 - 0.02 = 0.0146, \qquad \frac{\dot k_B}{k_B} = \frac{0.08}{2} - 0.02 = 0.04 - 0.02 = 0.02.
  5. 5

    Halving these gives the growth rates of yy:

  6. 6
    y˙AyA≈0.0073,y˙ByB=0.01. \frac{\dot y_A}{y_A} \approx 0.0073, \qquad \frac{\dot y_B}{y_B} = 0.01.
  7. 7

    Hence yy grows faster in BB than in AA.

Answer structure / marking notes

Both economies are below their respective steady states, but BB has a higher savings rate and a closer relative gap, so it grows faster.

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Content note

Imported from public/resources/isi/msqe/solutions/pea/2026/ISI_MSQE_PEA_2026_Solutions.tex. Question wording is retained from the available local TeX source; incomplete option blocks or ambiguous source status are flagged for review.