A closed economy can be described by the long-run classical model: Y = 3K^0.5L^0.5 C = 11000 + 0.8(Y - T) - 100r I(r) = 6000 - 100r Note: r is measured in percentage points (i.e., if r = 5, then r = 5%). Keep your answers to 2 decimal points if needed. Initially, the economy is endowed with 10000 units of capital and 40000 workers. The level of government spending is 8800, and the government runs a budget deficit of 800.

a) Compute the long-run equilibrium levels of consumption, investment, and real interest rate. Also, find the long-run equilibrium real wage for labour and real rental price of capital. (5 points).

Suppose the increasing use of automation leads to an increase in capital stock by 10.25%. b) Find the new equilibrium levels of output, real interest rate, and investment. (5 points)

c) Show your answers for parts (a) & (b) in three diagrams (that depict the loanable funds market, the labour market, and the rental market for capital in long-run equilibrium). Be sure to identify which points on your diagrams are the long-run equilibria for part (a) & (b) respectively. No written explanation is required. (9 points)

d) Suppose the government finds the change in the level of investment in part (b) undesirable and wants to keep to it at 4000 via a change in government spending. Find the level of government spending that could achieve the goal and the new budget balance. Comparing to your answer in part (b), what happens to the size of the budget balance (increase, decrease, or no change)? (6 points)