Question 3 (25 points) Consider a real intertemporal model with investment from Chapter 11 of the course textbook, modified to include public investment. The economy starts with the exogenous capital stock K and the public capital Ka Assume that public investment X made in the current period increases the quantity of the public capital stock in the future period, K's. Capital does not depreciate. So, the public capital evolves according to KG - KG +X Physical capital used in the production function follows the accumulation process Public investment and the public capital are taken as exogenous by consumers and firms. Assume that the public capital influences the level of total factor productivity in the same period. For example, an increase in Kincreases total factor productivity. All other features of the model are exactly as in Chapter 11. a) (5 points) The government must balance its budget in every period. Determine the government's budget constraints in the current and in the future periods. Explain your reasoning The government buys more investment goods in the current period. Analyze the effects of this exogenous increase in X on the competitive equilibrium, assuming that the public spending on public capital does not crowd our private investment. Use the subscript "1" to denote the variables in the initial equilibrium and the subscript"2" - in the new equilibrium b) 65 points) What effect, if any, does the increase in public investment X have on the positions of the labour supply and labour demand curves, given the initial market real interest rate n? Explain the economic reasons for the resulting impact in words, and relate your explanations to the assumptions about the consumer's preferences. c) (5 points) What effect, if any, does the increase in public investment X have on the position of the output supply curve given the initial market real interest rate n? Explain the economic reasons for the resulting impact in words, and relate your explanations to the model's assumptions. d) (5 points) What effect, if any, does the increase in public investment X have on the position of the outpur demand curve, given the initial market real interest rate n? Explain the economic reasons for the resulting impact in words, and relate our explanations to the model's assumptions c) 6 points) Determine the equilibrium effects of the increase in public investment on current aggregate output, current employment, the current real wage and the real interest rate. Illustrate your answer with the correctly labelled separate diagrams of the labour and goods markets. Explain the economic reasons for these effects in words