2 marksMicroeconomicsGeneral equilibrium and exchange economiesCompetitive equilibrium in an exchange economyHardabout 3 min

IIT JAM 2021 Question 51: General equilibrium and exchange economies

Amar has endowment $F_A = 2$ , $W_A = 5$ and utility $U_A = f_A^2 w_A$ . Barun has endowment $F_B = 8$ , $W_B = 5$ and utility $U_B = \min\{f_B, w_B\}$ . They trade food and water at prices $p_f$ and $p_w$ . In the competitive equilibrium, $\dfrac{p_f}{p_w}$ equals _______ (in integer).

Answer and worked solution

Answer: 2

Total endowments are $F = 10$ and $W = 10$ . Amar's utility $f_A^2 w_A$ gives Cobb-Douglas demands with food share $\tfrac23$ and water share $\tfrac13$ of his income $2p_f + 5p_w$ . Barun's Leontief utility gives $f_B = w_B = \dfrac{8p_f + 5p_w}{p_f + p_w}$ .

Normalising $p_w = 1$ and writing $\rho = p_f/p_w$ , water market clearing $\tfrac13(2\rho + 5) + \dfrac{8\rho + 5}{\rho + 1} = 10$ is solved by $\rho = 2$ (then Amar consumes $3$ water, Barun $7$ , summing to $10$ ; food splits $3$ and $7$ likewise). So $\dfrac{p_f}{p_w} = 2$ .

Plain-text version

Amar has endowment F_A = 2, W_A = 5 and utility U_A = f_A² w_A. Barun has endowment F_B = 8, W_B = 5 and utility U_B = min {f_B, w_B}. They trade food and water at prices p_f and p_w. In the competitive equilibrium, p_f/p_w equals _ (in integer).

Also written as: Amar has endowment F_A = 2, W_A = 5 and utility U_A = f_A^2 w_A. Barun has endowment F_B = 8, W_B = 5 and utility U_B = min {f_B, w_B}. They trade food and water at prices p_f and p_w. In the competitive equilibrium, p_f/p_w equals _ (in integer).

General equilibrium and exchange economies has come up 69 times in 7 exams since 2004.

What this question tests

This question is on Competitive equilibrium in an exchange economy, part of General equilibrium and exchange economies in Microeconomics.

Finding the prices at which every consumer's chosen bundle clears the market.

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