Question

(2) Solow Model Arithmetic: Suppose that the economy has the following production function: K >0 The population grows at the exogenously given rate n, so that N n)N (a) Derive the per worker production function, where y-Y/N is output per worker and k = K/N is capital per worker (b) Derive the aggregate accumulation equation for capital per worker expressed solely as a function of k. k', A, and parameters (s. θ, d, n). Recall the law of motion for capital: C-(1 - s)Y (c) Show that this accumulation equation is strictly concave (i.e. it has a second derivative with respect to k that is strictly less than 0) (d) Define the steady state (in words) (e) Derive an expression for the steady state capital stock per work as a function of A, d, s, θ, and n. (f) Derive an expression for the steady state consumption per worker (g) Find the saving rate, s, that maximizes steady state consumption per worker. To do this, take the derivative of your answer to part (d) with respect to s, set it equal to zero, and simplify, finding an expression for s as a function of the other parameters of the model

Answer 1

The given data is * consider my preference over-bundles (x_1, x_2) rightarrow where x_1 greaterthanorequalto 0 & x_2 greaterthanorequalto 0 rightarrow Here we have (1, 7) ~ (7, 5) a) (3, 7) > (1, 7) [as 1st good is max 3 > 1 and by assumption of strict monotonicity (b) (3, 7) > (1, 7) rightarrow And the (1, 7) ~ (7, 5) it is given by equation (3, 7) > (7, 5) by transitivity. (c) (1, 7) Vs (4, 6) (1, 7) ~ (7, 5) And the (0.5 times 1 + 0.5 times 7) (0.5 + 3.5) = 4 \r\n = (0.5 times + 0.5 times 5) = (3.5 + 2.5) = 6 rightarrow Then Here the (4, 6) is the convex combination of (1, 7) and (7, 5) rightarrow As my preference is strictly convex, convex combination of 2 indifferent bundle is at higher in in difference curve rightarrow then (1, 7) < (4, 6) (d) As the (1, 7) < (4, 6) (7, 5) < (4, 6), as (1, 7) ~ (7, 5)