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Consider the following production function: y = F(K, L, D) = TK^αL^β/D^α+β−1 where K, L and...

Consider the following production function: y = F(K, L, D) = TK^αL^β/D^α+β−1 where K, L and D represent capital, labor and land inputs respectively. Denote by s the capital-labor ratio (s = K L ). T captures technological progress and is assumed constant here. α and β are two parameters. (a) (2.5 marks) Does y exhibits constant returns to scale? Show your work. (b) (2.5 marks) Find the marginal product of capital (MPK), the marginal product of labor (MP L), and the marginal propensity of land (MP D). (c) (2.5 marks) Show that Euler’s theorem holds for this production function. (d) (2.5 marks) Consider the function H = e √ (y) + 2. Is H homothetic? (if any restrictions should be imposed, state them clearly).

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