Consider a one-period closed economy of Kingdom of Bebbanburg that consists of numerous households that have identical preference structures, U(c, I), where c is the consumption, / is leisure. The preference structure of the households is well-behaved (i.e. indifference curves that represent the preferences are negatively sloped, convex to the origin, do not intersect and are parallel to each other; also, utility increases for higher indifference curves further away from the origin). The households have a limited amount of time at their disposal, h, and have the choice to use it conducting leisurely activities that provide them utility (sleeping, going out, fishing, exercising, etc.) or work (let the labor supply of households be N) and get paid the market wage w. Each household also owns an equal share of the firms in this economy and get profit income (dividend) from them. There is also a government run by Lord Uhtred that uses lump-sum taxation to extract T from the households, to finance its expenditures G. Government budget is assumed to be balanced at all times, G-T. Production of the consumption good in the economy of Bebbanburg is made possible by a large number of identical firms that have the following production technology, where K is the fixed capital stock of the economy, N is employment and z is the exogenous technology or Total Factor Productivity (TFP) parameter, and 0 < a < 1, Y = zf (K,N) = ZKaN-a Households and firms interact in the labor market by exchanging labor in return for wages (note that this is a real-economy and wages are paid in terms of consumption goods, i.e. w-2 means one unit of labor will deliver you 2 units of the consumption good). Households, firms and the government also interact in the goods market, and the national income identity holds in equilibrium. a) (5 points) What are the exogenous variables in this model? What are the endogenous variables? What are the given (exogenous) parameters of the model? b) (5 points) Define the competitive equilibrium of this economy; be precise as in your textbook (Definition hint: A competitive equilibrium is a list of endogenous variables....). c) (8 points) Write down the budget and time constraint of the representative household. Write down the utility maximization problem of the representative household. What are the choice variables of the household? d) (8 points) Write down the profit maximization problem of the representative firm, what does the firm choose by maximizing profit? e) (8 points) On an appropriate graph, depict the general equilibrium of this economy (showing the PPF, the household budget constraint and the indifference curves). f) (16 points) Suppose now that the Kingdom of Bebbanburg receives a gift from the friendly neighboring Kingdom of Mercia, which substantially increases the nation's capital stock, K. In the model given above, a. (8 points) Determine the effect of this exogenous increase in capital stock on aggregate output, consumption, employment and real wage in Bebbanburg, with reference to income and substitution effects, and explain your results. Do not forget to show the effects in the labor market (i.e. show first how the marginal productivity of labor is affected after the increase in capital stock, and how this affects the equilibrium in the labor market) b. (8 points) Show the change in the general equilibrium of the economy using the PPF (showing the initial and the final equilibria), the household budget constraint and the indifference curves. In doing so, explain how the shape of PPF is affected and how the budget constraint is affected (both in terms of the position and the slope of the budget constraint). Finally, show the new general equilibrium of the economy after the exogenous change in capital stock.