Homework Answers
Therefore, by derivative of y with respect to t states that the growth rate of GNP depends on the capital held at time t (which can be 1,2,3...n). The findings has suggested that the growth rate is a function of capital and is positively related with capital. As the capital is increased by 10 percent the growth rate of GNP will be by 5 percent.
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78. Suppose both that the amount of capital at time t, K-K(t), and that the efficiency...
Suppose output, Y t, is produced using capital, K t, and labor, N t, according to...
Suppose output, Y t, is produced using capital, K t, and labor, N t, according to the production function: Y t = A ⋅ ( K t α N t 1 − α + K t β N t 1 − β )where the parameters satisfy 0 < α < 1, 0 < β < 1 and A > 0. a) (5 pts) Write the production function in “per worker” terms. That is, if we define y t = Y...
Suppose that the growth of the national economic output of a country Y depends on how much capita...
Mathematical Economics:
Suppose that the growth of the national economic output of a country Y depends on how much capital K is available in the economy and also on the progress of technolog- ical innovation g according to the following aggregate production function: Y(g, K) 0.5gK. Suppose furthermore that the evolution of technological growth and that of the aggre- gate capital stock over time t are given as g(t) V1+t, K(t) 10e0.02t. The chain rule tells us that the total...
(2) Solow Model Arithmetic: Suppose that the economy has the following production function: K >0 The...
(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...
(2) Solow Model Arithmetic: Suppose that the economy has the following production function K >O The...
(2) Solow Model Arithmetic: Suppose that the economy has the following production function K >O The population grows at the exogenously given rate n, so that N-(1+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, ,A, and parameters (s,8, d,n). Recall the law of motion for capital: (e) Show...
(2) Solow Model Arithmetic: Suppose that the economy has the following production function: K > 0...
(2) Solow Model Arithmetic: Suppose that the economy has the following production function: K > 0 n > The population grows at the exogenously given rate n, so that N,-(1 + 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...
Differentiate. 18) y 4ex2 Solve the problem. 19) Suppose that the amount in grams of a radioactive substance presen...
Differentiate. 18) y 4ex2 Solve the problem. 19) Suppose that the amount in grams of a radioactive substance present at time t (in years) is given by A(t)-550e-0.79t, Find the rate of change of the quantity present at the time when t -7. Find the derivative of the function. In 7x2 20) y 21) y- Solve the problem. 22) A CD store determines the following demand function for a particular album q Dx)-V470-x2, where q- the number of CDs sold...
5. Suppose that an economy has a fixed amount L* of homogeneous labour, and a fixed amount K*of h...
5. Suppose that an economy has a fixed amount L* of homogeneous labour, and a fixed amount K*of homogeneous capital, to be used in producing outputs x and y) In an Edgeworth box having dimensions L and K* in input space, suppose the inputs are the absolute slope of the x isoquant (i.e., the marginal rate of technical substitution) is 1K/2L and the absolute slope of the y' isoquant (i.e., the marginal rate of technical substitution) İs l K/L indicate...
Consider the Solow growth model that we developed in class. Output at time t is given...
Consider the Solow growth model that we developed in class. Output at time t is given by the production function Y AK Lt, where A is total factor productivity, Kt is total capital at timet and L is the labour force. Total factor productivity A and labour force L are constant over time. There is no government or foreign trade and Y, + 1, where Ct is consumption and I is investment at tim. Every agent saves s share of...
Homework #1 1. Suppose that a variable Z(t) x(t)/y(t). Prove that for Zlt) to be constant,...
Homework #1 1. Suppose that a variable Z(t) x(t)/y(t). Prove that for Zlt) to be constant, x and y must grow at the same rate. To do this, take the natural logarithm of both sides and differentiate with respect to time. (If a variable is constant, its time derivative is zero)
3. Yasmin (Y) and Xavier (X) run firms that produce goods using capital (K) and labor...
3. Yasmin (Y) and Xavier (X) run firms that produce goods using capital (K) and labor (L). They each have technologies such that the Marginal Product of Capital is given by L (the amount of labor hired by the firm) and the Marginal Product of Labor is given by K (the amount of capital used by the firm). Thus, for Yasmin, the marginal rate of technical substitution for her firm is given by where the subscript indicates that this is...
Mathematical Economics:
Suppose that the growth of the national economic output of a country Y depends on how much capital K is available in the economy and also on the progress of technolog- ical innovation g according to the following aggregate production function: Y(g, K) 0.5gK. Suppose furthermore that the evolution of technological growth and that of the aggre- gate capital stock over time t are given as g(t) V1+t, K(t) 10e0.02t. The chain rule tells us that the total...
(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...
(2) Solow Model Arithmetic: Suppose that the economy has the following production function K >O The population grows at the exogenously given rate n, so that N-(1+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, ,A, and parameters (s,8, d,n). Recall the law of motion for capital: (e) Show...
(2) Solow Model Arithmetic: Suppose that the economy has the following production function: K > 0 n > The population grows at the exogenously given rate n, so that N,-(1 + 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...
Differentiate. 18) y 4ex2 Solve the problem. 19) Suppose that the amount in grams of a radioactive substance present at time t (in years) is given by A(t)-550e-0.79t, Find the rate of change of the quantity present at the time when t -7. Find the derivative of the function. In 7x2 20) y 21) y- Solve the problem. 22) A CD store determines the following demand function for a particular album q Dx)-V470-x2, where q- the number of CDs sold...
5. Suppose that an economy has a fixed amount L* of homogeneous labour, and a fixed amount K*of homogeneous capital, to be used in producing outputs x and y) In an Edgeworth box having dimensions L and K* in input space, suppose the inputs are the absolute slope of the x isoquant (i.e., the marginal rate of technical substitution) is 1K/2L and the absolute slope of the y' isoquant (i.e., the marginal rate of technical substitution) İs l K/L indicate...
Consider the Solow growth model that we developed in class. Output at time t is given by the production function Y AK Lt, where A is total factor productivity, Kt is total capital at timet and L is the labour force. Total factor productivity A and labour force L are constant over time. There is no government or foreign trade and Y, + 1, where Ct is consumption and I is investment at tim. Every agent saves s share of...
Homework #1 1. Suppose that a variable Z(t) x(t)/y(t). Prove that for Zlt) to be constant, x and y must grow at the same rate. To do this, take the natural logarithm of both sides and differentiate with respect to time. (If a variable is constant, its time derivative is zero)
3. Yasmin (Y) and Xavier (X) run firms that produce goods using capital (K) and labor (L). They each have technologies such that the Marginal Product of Capital is given by L (the amount of labor hired by the firm) and the Marginal Product of Labor is given by K (the amount of capital used by the firm). Thus, for Yasmin, the marginal rate of technical substitution for her firm is given by where the subscript indicates that this is...
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