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Given demand function: Qdt = 1200 − 6Pt

Computer Science

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Answer

i

N90\text{N}90

660 units660 \text{ units}

Step-by-step solution

5 steps

Here's a step-by-step solution for the market analysis:

Given demand function: Qdt=1200−6PtQd_t = 1200 - 6P_t
Given supply function: Qst=300+4Pt−1Qs_t = 300 + 4P_{t-1}

Part i· 3 steps

Determine the equilibrium condition of the market

  1. Set demand equal to supply to find the equilibrium price PeP_e.

    At equilibrium, Qdt=QstQd_t = Qs_t and Pt=Pt−1=PeP_t = P_{t-1} = P_e.

    1200−6Pe=300+4Pe1200 - 6P_e = 300 + 4P_e
  2. Solve for PeP_e.

    1200−300=4Pe+6Pe1200 - 300 = 4P_e + 6P_e 900=10Pe900 = 10P_e Pe=90010P_e = \frac{900}{10} Pe=90P_e = 90

    The equilibrium price is N90.

  3. Substitute PeP_e into either the demand or supply equation to find the equilibrium quantity QeQ_e.

    Using the demand equation:

    Qe=1200−6(90)Q_e = 1200 - 6(90) Qe=1200−540Q_e = 1200 - 540 Qe=660Q_e = 660

    The equilibrium quantity is 660 units.

    The equilibrium condition of the market is:

    • Equilibrium Price (PeP_e): N90\boxed{\text{N}90}
    • Equilibrium Quantity (QeQ_e): 660 units\boxed{660 \text{ units}}

Part ii· 2 steps

Determine the stability condition of the market

  1. Derive the dynamic price equation by setting Qdt=QstQd_t = Qs_t.

    1200−6Pt=300+4Pt−11200 - 6P_t = 300 + 4P_{t-1}

    Rearrange the equation to express PtP_t in terms of Pt−1P_{t-1}:

    6Pt=1200−300−4Pt−16P_t = 1200 - 300 - 4P_{t-1} 6Pt=900−4Pt−16P_t = 900 - 4P_{t-1} Pt=9006−46Pt−1P_t = \frac{900}{6} - \frac{4}{6}P_{t-1} Pt=150−23Pt−1P_t = 150 - \frac{2}{3}P_{t-1}
  2. Identify the coefficient of Pt−1P_{t-1} and check the stability condition.

    The dynamic equation is in the form Pt=A+λPt−1P_t = A + \lambda P_{t-1}, where λ\lambda

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