(e) Now, assume there is no population growth in this economy, i.e. NU) = N. Use the definition of the total output growth rate to nd the relationship between the growth rate of total output, gy, and 9K. Question 2: Learning-by-doing and endogenous growth [25 Marks] This question explores the idea of learning-by-doing as a source of economic growth. Consider the same production function as in the last part of Question 1: Y(t) = K(t) [A(t) N(t) ]1-a, (2) where, as before, Y(t) denotes output, K(t) denotes total capital input, and N(t) denotes total labour input. Capital depreciates at a rate d. The key deviation from the last part of Question 1 regarding the production side of the economy is that "knowledge" A(t) is now proportional to the capital stock, in particular, A(t) = BK(t), (3) where B is a positive coefficient. This specification is designed to capture the idea of learning-by-doing: a greater capital stock increases the scale of production and the expe rience (of workers, managers, etc) accumulated with production processes, making the production process itself more productive. (a) Substitute Equation 3 into Equation 2] and verify the similarity of this model to the textbook AK model. (b) Calculate the growth rate of the capital stock K(t), assuming that saving in this econ- omy is proportional to total output, i.e. S(t) = sY(t), and the goods market is in equilib rium. Define the answer you get in this part as gx. [Hint: Use the relationship between net and gross investment in Chapter 4.]