Microeconomics · Hard · 30 marks
IEO past paper: 2021 International Economics Olympiad, open questions
Oil (good A) and Gas (good B) are substitutes in consumption; the demand and supply functions are given by:
Good Demand Supply Oil (A) D A = K − 2 P A + P B S A = − 10 + 2 P A Gas (B) D B = 80 − 6 P B + 2 P A S B = − 5 + P B \begin{array}{lll} \text{Good} & \text{Demand} & \text{Supply} \\ \hline \text{Oil (A)} & D_A = K - 2P_A + P_B & S_A = -10 + 2P_A \\ \text{Gas (B)} & D_B = 80 - 6P_B + 2P_A & S_B = -5 + P_B \end{array} Good Oil (A) Gas (B) Demand D A = K − 2 P A + P B D B = 80 − 6 P B + 2 P A Supply S A = − 10 + 2 P A S B = − 5 + P B
(a) Find equilibrium prices P A ∗ P_A^* P A ∗ P B ∗ P_B^* P B ∗ K = 210 K = 210 K = 210 [5] marks (b) Now consider a dynamic version of this model. We consider the demand for Gas constant for simplicity, but the demand for Oil is volatile. In period t t t K K K K t K_t K t K 1 = 210 K_1 = 210 K 1 = 210 t = 1 t = 1 t = 1 K 2 K_2 K 2 [10] marks (c) The prediction of demand decline turned out to be wrong, so K 2 K_2 K 2 [5] marks (d) Suppose that starting from period 2, firms' expectations are naive. This means that they always expect the next period's prices to equal the prices in the current period and make decisions about future production based on this prediction. At the same time, the actual value of K K K t → ∞ t \to \infty t → ∞ [10] marks
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