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MIDTERM EXAM PRACTICE QUESTIONS QUESTION-1: Consider the general Solow growth model. Suppose production function at time t is described as: where Yt is aggregate output, Kt is aggregate capital stock, Lt is total population or labour force and At is technical progress enters in the production function, as labour-augmenting technology (also known as the effectiveness of labour). Suppose At+1= (1+g)At and Lt+1=(1+n)Lt, and the capital accumulation is given as: . A) Derive the per effective worker form production function. B) Define the balanced growth path. Using above growth model to drive the growth rates of Y, K, y=Y/L, k=K/L, , and at the BGP. C) Use the above general Solow growth model to derive the law of motion equation. D) Drive the steady state values for output, capital and consumption per effective worker i.e. , and . E) Assume the values of parameters given as: s = 0.20, g = 0.02, n = 0.01, δ = 0.05 and α =0.25 What is the value of , and ? Draw a diagram to show steady values. F) Use the above general Solow model to derive the golden rule saving rate. Use part (E) to calculate golden rule saving rate and golden rule capital per effective worker value in the steady state i.e. . Draw a diagram to explain the results in this part using appropriate labels of the curves. G) Using (E) and (F), what happens to the saving rate s=0.20 when it is compared with ? H) Derive the labour share of income from the above given production function. What are the values of labour and capital shares of income (no calculation required)? I) Why growth rate of output per worker is sustainable in Solow model with technology versus without technology? QUESTION-2: Consider the Solow growth model. Suppose the economy starts on a BGP and then the savings rate increases permanently. A. What is the impact on the long-run values of the capital stock and output per unit of effective worker, and respectively, and the long-run of growth rate of output per capita (). Explain by using diagram. B. Consider the following discrete time version of the Solow growth model. Suppose production is described by . The production function exhibits constant returns to scale. The intensive form of the production function is concave and satisfies the Inada conditions. Suppose also that , and . Find an expression for the capital stock per unit of effective labour, as a function of. Show your complete work as done in class. QUESTION-3: A) What is the difference between absolute and conditional convergence? B) Stylized facts state that countries with lower initial capital per worker will grow faster than countries with higher initial capital per worker. Comment. C) QUESTION-4: A) The version of Solow equation with human capital is given as: Take log of the above equation and answer the following questions based on the log equation. i) What is the elasticity of with respect to and with and without human capital? If , what are the elasticity values and which of the elasticity is larger, interpret the result. ii) Give interpretation to the above equation when . iii) How do you interpret the influence of population growth on Solow model with and without human capital? Explain. B) Suppose that output , Y, is produced by combination of physical capital, K, and with skilled labor, H, according the CRS, Cobb-Douglas production function is: where A represents labor-augmenting technology that grows exogenously at rate g. where μ denotes the faction of an individual’s time spent learning skills, ψ is positive constant and L is total amount of labour. H/L = h. The physical capital accumulation equation is given as: where is the investment rate for phusical capital and is the constant depreciation. (i) Derive the above production function to write in the per effective worker form. (ii) Suppose law of motion is derived from the above equation system is: . Use law of motion to derive the steady state value of output per worker y* (note: it is not output per effective per worker). AL Y y = ~ AL K k = ~ * ~ y * ~ k * ~ c * ~ GR k k ~ y ~ y ˆ ( ) t t t t L A K F Y , = t t A g A ) 1 ( 1 + = + t t L n L ) 1 ( 1 + = + t t K sY K d - = & 1 + t k t k a a - = 1 ) ( t t t t L A K Y t t t t K sY K K K d - = - = + 1 &