The following are the questions890

Part C Human Capital and the Romer Model Consider the following standard Homer Model and a variation that includes human capital. Human Capital Goods Production Function K: = .4th Ideas Production Function AAH1 = iAgH 1L.\" Human Capital Production Function Ht : Lb; Resource Constraint Allocation of Labour 1. Explain what using labour to produce human capital implies for the economy? 2. Solve for the balanced growth path of output per capita in both models, showing all working. 3. Does the inclusion of human capital increase the rate of growth compared to the standard model? What is the impact on output in the short and long run? Discuss the solution of the Standard Dolow Model using the production function *+ = AK +" Held Where K+ + stock of Physical Capital Ht - stock of Human Lafital A - General Productivity Level Does there exist a unique I stable steady State ? If yes, then show it.6. The Mankiw-Romer-Weil (1992) model. As mentioned in this chap- ter, the extended Solow model that we have considered differs slightly from that in Mankiw, Romer, and Weil (1992). This problem asks you to solve their model. The key difference is the treatment of human capital. Mankiw, Romer, and Weil assume that human capi- tal is accumulated just like physical capital, so that it is measured in units of output instead of years of time. Assume production is given by Y = KoHB(AL)1-@-8, where a and B are constants between zero and one whose sum is also between zero and one. Human capital is accumulated just like physical capital: H = SHY - 8H.where sy is the constant share of output invested in human capital. Assume that physical capital is accumulated as in equation (3.4), that the labor force grows at rate n, and that technological progress occurs at rate g. Solve the model for the path of output per worker y = Y/L along the balanced growth path as a function of SK, SH, n, g, 6, a, and B. Discuss how the solution differs from that in equation (3.8). (Hint: define state variables such as y/A, h/ A, and k/ A.)Question 2: Capital formation in growth models 10 points each sub-part molly weighted LDBI'ive the capital formation equation for HEII'Dd Domai- model. 2.Derive the capital formation equation for Solow model with and without labor augmenting technological progress. 3.Derive the human capital formation equation for the following production function Y = HK5(TL)'*\"*\" where Y is output, H is human capital in the production function, K is physical capital used in the production function and L is labor. The saving rate in human capital is given by s. Human Capital: Our textbook points out that human capital is not included in the simple model of production but that it could be an important factor in explaining why the marginal product of capital differs among countries. 1. Consider a Cobb-Douglas production function with three inputs: Y = KiLiHi, (1) where K is capital, L is labor, and H is human capital. What is the marginal product of capital (MPK) implied by this production function? 2. Is MPK increasing in human capital or decreasing? 3. Use this model to explain why capital may flow from poor to rich countries. 4. Is the return to education higher or lower in countries with scarce capital?(b) A noisy binary communication channel randomly corrupts bits with probability p, so its channel matrix is: 1 - P P p 1- p (f) If the input bit values {0,1} are equiprobable, what is the mutual information between the input and output for this noisy channel? (2 marks] (ii) What is the channel capacity of this noisy channel? [1 mark] (in) If an error-correcting code were designed for this noisy channel, what would be the maximum possible entropy of an input source for which reliable transmission could still be achieved? Express your answer in terms of p. [1 mark]