Suppose we have an economy with the following aggregate production function: Y = K" (AN) + E' Y stands for output, K for the capital stock, N for the number of people employed in production, E for the quantity of energy used in production, and A for a measure of labour efficiency. The coefficients a, and y are parameters whose values are between 0 and 1. Suppose = = y = 0.5. Based on the production function, derive an algebraic expression for the demand for labour, assuming that w is the real wage. Be sure to sub in the values for a and as this will simplify your final relationship. Now suppose that the supply curve is upward-sloping and has the following form: N = w Find an algebraic equation for the equilibrium real wage, w, and equilibrium employment, . Now suppose, A = 4; K = 16; and E = 1. Compute the values for the equilibrium real wage, w, equilibrium employment, , and the level of full employment output, Y. Use 2 decimals if needed. Suppose there is a negative supply shock and A decreases to 3. Find the new values for the equilibrium real wage, w, equilibrium employment, , and the level of full employment output, Y. Use 2 decimals if needed. Also, show this shock using 2 graphs: one for the labour market and another for the production function. Instead of the supply shock of part d), let's suppose the country invests heavily in energy infrastructure and the quantity of energy quadruples to E = 4. Find the new values for the equilibrium real wage, w, equilibrium employment, , and the level of full employment output, . Use 2 decimals if needed.