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2024 PEA Q29

Country CC has 10,00010{,}000 identical farmers with cost C(qi)=0.5qi2+4qi+100C(q_i)=0.5q_i^{2}+4q_i+100, aggregate demand Q=−10,000p+400,000Q=-10{,}000p+400{,}000. Current price support p=30p=30; government buys all unsold output at 3030. The government proposes removing the support and giving each farmer an equal share of the saved expenditure as a lump-sum transfer. Each farmer must, however, pay 300300 to open a bank account to receive the transfer. By how much does a farmer gain (or lose)?

Reveal answer and solution

Answer

B

Solution

  1. 1

    Per-farmer profit under price support (p=30p=30): A competitive farmer chooses qq s.t.\ p=MC(q)=q+4⇒q=26p=MC(q)=q+4\Rightarrow q=26. Revenue =30⋅26=780=30\cdot 26=780; cost =0.5⋅676+4⋅26+100=338+104+100=542=0.5\cdot 676+4\cdot 26+100=338+104+100=542. Profit πR=780−542=238\pi^{R}=780-542=238.

  2. 2

    Government's purchase cost under support: At p=30p=30 consumers buy Qd=−10,000(30)+400,000=100,000Q^{d}=-10{,}000(30)+400{,}000=100{,}000. Farmers' aggregate output is 10,000⋅26=260,00010{,}000\cdot 26=260{,}000. Government buys 260,000−100,000=160,000260{,}000-100{,}000=160{,}000 units at 3030, total expenditure =30⋅160,000=4,800,000=30\cdot 160{,}000=4{,}800{,}000. Per-farmer share of savings =4,800,000/10,000=480=4{,}800{,}000/10{,}000=480.

  3. 3

    Competitive equilibrium after deregulation: Aggregate supply qs=10,000(p−4)q_{s}=10{,}000(p-4). Setting qs=Qdq_{s}=Q^{d}:

  4. 4
    10,000(p−4)=−10,000p+400,000 ⟹ 20,000p=440,000 ⟹ p∗=22, qi∗=18. 10{,}000(p-4)= -10{,}000p+400{,}000\ \Longrightarrow\ 20{,}000p=440{,}000\ \Longrightarrow\ p^{*}=22,\ q^{*}_i=18.
  5. 5

    Profit πC=22⋅18−(0.5⋅324+4⋅18+100)=396−(162+72+100)=396−334=62\pi^{C}=22\cdot 18 -(0.5\cdot 324+4\cdot 18+100)=396-(162+72+100)=396-334=62.

  6. 6

    Net change in farmer's income:

  7. 7
    Δ=πC−πR+480−300=62−238+480−300=4. \Delta = \pi^{C}-\pi^{R}+480-300 = 62-238+480-300=4.
  8. 8

    So each farmer is better off by 44.

Answer structure / marking notes

Don't forget to subtract the bank-account cost of 300300.

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Content note

Imported from public/resources/isi/msqe/solutions/pea/2024/ISI_MSQE_PEA_2024_Solutions.tex. Question wording is retained from the available local TeX source; incomplete option blocks or ambiguous source status are flagged for review.