# 1. Let the aggregate production function of an economy be given byY = K (AN)1 (a) (10 points) If = 1/3, and output per worker grows at 2% and capital…

1. Let the aggregate production function of an economy be given byY = Kα (AN)1−α

(a) (10 points) If α = 1/3, and output per worker grows at 2% and capital per worker grows at 3%, what is the technological change in this economy?

(b) (10 points) Explain the intuition behind the Solow Residual.

2. Consider an open economy characterized by the equations

C = c0 + c1 (Y − T )

IM = m1Y X = x1Y ∗

where G = Ḡ, T = T̄, I = Ī and Y ∗ = Ȳ ∗.

(a) (10 points) Write the equilibrium condition in the market for domestic goods and solve for Y.

(b) (10 points) Suppose foreign output falls by one unit. What is the effect on domestic output? Show algebraically, graphically and explain the intuition.

3. Consider an economy that suffers a fall in business confidence (which tends to reduce investment). Let UIP stand for the Uncovered Interest Parity condition.

1. (a) (10 points) Suppose the economy has a flexible exchange rate. In an IS-LM-UIP diagram, show the short-run effect of the fall in business confidence on output, the interest rate, and the exchange rate.
2. (b) (10 points) Suppose instead the economy has a fixed exchange rate. In an IS-LM-UIP diagram, show how the economy responds to the fall in business confidence.
3. (c) (10 points) Explain how the exchange rate acts as an automatic stabilizer in an economy with flexible exchange rates.