1. Xanadu is a perfectly competitive economy with K amount of capital and I amount of...

  

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1. Xanadu is a perfectly competitive economy with K amount of capital and I amount of labour. All factors of production are fixed and fully employed. Technology is described by a Cobb-Douglas production function given by: Y = F(K,L) = AKaīb (6) a) For each of the following cases, indicate whether the production function exhibits increasing, decreasing or constant returns to scale. Demonstrate your result (by introducing a "multiple z" of the factors of production) and explain. (You may choose z = 2). i) a= 0.4, b=0.5 ii) a= 0.3, b=0.7 iii) a = 0.6, b=0.6 (6) b) Suppose that a = 0.4, b=0.6. If factors are paid their marginal products, what is the share of income received by capital and labour, respectively? Show your result and explain. (5) c) The labour force in Xanadu is 100 and the capital stock is 60. The technology parameter A is 50. If all labour and capital resources are fully utilized, how much output is produced in Xanadu? (24) d) Unfortunately, a strong earthquake (5.9 on the Richter scale) destroyed 20% of Xanadu's capital. However, thanks to the very strict construction laws in the country, the population was not harmed, and the labour force remained unchanged. (Assume again that a = 0.4, b=0.6). (i) What is the new total output level in Xanadu? By how much has it changed? Calculate. (Round off to the nearest whole number.) Explain the change in words (i.e., is it higher or lower than the initial value, and why?). Draw a graph of the production function with K on the horizontal axis to illustrate the change. Show your work. (ii) (iii) What is the new real rental rate? Calculate both the initial and the new real rental rate ₁ and 2 respectively. (Round off to the nearest whole number.) Explain the change in words (i.e., is it higher or lower than the initial value, and why?) Draw a graph of the capital market to illustrate. What is the new real wage rate. Calculate both the initial and the new real wage rate ₁ and ₂ respectively. (Round off to the nearest whole number.) Explain the change in words (i.e., is it higher or lower than the initial value, and why?) Draw a graph of the labour market to illustrate. Show your work. Explain in words. In each case, indicate the direction of change (increase or decrease) on your graphs. 1. Xanadu is a perfectly competitive economy with K amount of capital and I amount of labour. All factors of production are fixed and fully employed. Technology is described by a Cobb-Douglas production function given by: Y = F(K,L) = AKaīb (6) a) For each of the following cases, indicate whether the production function exhibits increasing, decreasing or constant returns to scale. Demonstrate your result (by introducing a "multiple z" of the factors of production) and explain. (You may choose z = 2). i) a= 0.4, b=0.5 ii) a= 0.3, b=0.7 iii) a = 0.6, b=0.6 (6) b) Suppose that a = 0.4, b=0.6. If factors are paid their marginal products, what is the share of income received by capital and labour, respectively? Show your result and explain. (5) c) The labour force in Xanadu is 100 and the capital stock is 60. The technology parameter A is 50. If all labour and capital resources are fully utilized, how much output is produced in Xanadu? (24) d) Unfortunately, a strong earthquake (5.9 on the Richter scale) destroyed 20% of Xanadu's capital. However, thanks to the very strict construction laws in the country, the population was not harmed, and the labour force remained unchanged. (Assume again that a = 0.4, b=0.6). (i) What is the new total output level in Xanadu? By how much has it changed? Calculate. (Round off to the nearest whole number.) Explain the change in words (i.e., is it higher or lower than the initial value, and why?). Draw a graph of the production function with K on the horizontal axis to illustrate the change. Show your work. (ii) (iii) What is the new real rental rate? Calculate both the initial and the new real rental rate ₁ and 2 respectively. (Round off to the nearest whole number.) Explain the change in words (i.e., is it higher or lower than the initial value, and why?) Draw a graph of the capital market to illustrate. What is the new real wage rate. Calculate both the initial and the new real wage rate ₁ and ₂ respectively. (Round off to the nearest whole number.) Explain the change in words (i.e., is it higher or lower than the initial value, and why?) Draw a graph of the labour market to illustrate. Show your work. Explain in words. In each case, indicate the direction of change (increase or decrease) on your graphs.

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a To determine whether the production function exhibits increasing decreasing or constant returns to scale we need to examine the exponents of capital a and labor b i For a 04 and b 05 The production ... View the full answer