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Question 1 (20 marks) Consider an economy with population P. The output in this economy is given by the production function Y = KaLla where, L = XP and X is the labour force participation rate, i.e., the proportion of population in the economy who work. K, as earlier, is the capital stock. Capital stock and population in this economy evolve according to the following equations K=sY6K a\" i. Calculate the steady state capital stock per capita and output per capita in this economy, i.e., k and y. (7 marks) [Hintz Carefully recall what 'per capita' is] ii. Show this steady state graphically. Explain the construction of your graph clearly. (3 marks) iii. Suppose that at time t = 0, the economy is in a steady state. In this steady state, all men work but only 25% of the women in the economy work. Assume that men and women each make up half the population in the economy and have the same population growth rate. At time t = 1, all men still work but 50% women start working. What is the new steady state output per capita if the per capita output at t = 0 is yo? (5 marks) iv. Show the transition to this new steady state graphically. Explain what happens as soon as the labour force participation rate rises and then how does the economy move after