Consider a setting in which buyers and sellers match bi-laterally in housing market. Let B denote...

 

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Consider a setting in which buyers and sellers match bi-laterally in housing market. Let B denote the number of potential buyers searching and S then number of sellers each which a single vacant house for sale. Let the number of matches each period between buyers and sellers be given by: M(B, S) = ABS-a 0 < a < 1. (1) a. Let 0 denote market tightness and find the probabilities of matching for both buyers and sellers. b. What happens to the number of matches as market tightness tends to infinity? c. Derive n(0), the elasticity of the number of matches, M(B, S), with respect to the number of sellers/vacancies, S. d. If matches are formed according to (1) and sellers post prices according to the process of directed search, how does the sellers' share of the surplus in housing transactions vary with market tightness, 0? Consider a setting in which buyers and sellers match bi-laterally in housing market. Let B denote the number of potential buyers searching and S then number of sellers each which a single vacant house for sale. Let the number of matches each period between buyers and sellers be given by: M(B, S) = ABS-a 0 < a < 1. (1) a. Let 0 denote market tightness and find the probabilities of matching for both buyers and sellers. b. What happens to the number of matches as market tightness tends to infinity? c. Derive n(0), the elasticity of the number of matches, M(B, S), with respect to the number of sellers/vacancies, S. d. If matches are formed according to (1) and sellers post prices according to the process of directed search, how does the sellers' share of the surplus in housing transactions vary with market tightness, 0?

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Step 12 a The probabilities of matching for buyers and sellers are given by Pmatch for buyers ABSa A... View the full answer