ECON 385

Intermediate Macroeconomic Theory II, Fall 2024

Midterm Exam

1. (15 points) Consider the DMP model. Weakening of labor unions leads to a reduction in the worker’s bargaining power, a; at the same time, the cost of posting a vacancy, k, goes down.

(a) (5 points) Analyze the changes using the relevant diagrams, clearly labeling axes and showing all the relevant values on the x-axis and y-axis before and after the changes in the worker bargaining power and unemployment insurance benefit.

(b) (10 points) Discuss economics behind the possible e↵ects of changes on i) labor market tightness; ii) unemployment rate; iii) labor force; (iv) the vacancy rate,

(v) aggregate output, and (vi) the wage. (The full mark will be given only to answers that comment on the changes—simply stating direction of the change will be not enough.)

2. (20 points) Provide short answers to each question below.

(a) (5 points) Does the production function

Y = K1/5 L4/5 − A KL

exhibit increasing, constant, or decreasing returns to scale in K and L? Assume A is a fixed positive number. (Note: Show your work. Simply guessing it correctly will not yield any points.)

(b) (5 points) Let us make a conjecture that technology levels are the same across countries so that the di↵erences in GDP per capita are the result of di↵erences in capital per capita. Let the ratio of capital per worker in the UK relative to the U.S. value equal 0.832. Assume that production function for the U.S. and UK is Cobb-Douglas, constant-returns-to-scale in capital and labor, with the share of capital costs in total income being equal to 1 3 . What would be the predicted ratio of real wages in the UK relative to the U.S. value?

(c) (5 points) Assume a Solow economy with no technological progress. Production function is Cobb-Douglas. The share of capital income in total income equals 50%. Population growth equals 2% and the depreciation rate equals 3%. The savings rate in the economy is 10%. What is the ratio of output per capita in the steady-state of the economy with the savings rate of 10% relative to the value of output per capita in the golden rule steady state?

(d) (5 points) Consider a Solow economy with population growth and technological progress. Prove that in the steady state (balanced growth path) the capital-output ratio is constant in this economy

3. (15 points) Consider an economy experiencing a reduction in the aggregate capital from K0 to K1 < K0 at some point in time t0 (due to, e.g., a war). Assuming the economy with technological progress at a rate of 3% and population growth of 3% starts in its initial steady state, use the Solow model to explain in words what happens to the economy over time and in the very long run. Support your answer with three diagrams: 1) the Solow diagram that outlines the changes; 2) output per capita against time using a ratio scale and 3) total output against time using a ratio scale. Assume that the growth rate of population stays constant over time at a rate of 3%.