INTER MACROECONOMIC THEORY

ECON2213 - Assignment #1 - Due September 22nd

1. Justify, in words, why MPL=w and MPK=R within a perfect labor market and a perfect capital market, respectively.

2. Suppose Canada annexes Greenland. Within the perfect factor markets framework discussed in Ch.3, explain what would likely happen to w, R, and Y . State any assumptions you make.

3. Consider a production economy as per class/Mankiw Ch.3 with some standard production function and some fixed capital stock, K, and fixed labor force, L. Suppose an earthquake destroys a chunk of the capital stock. What happens to Y ,r and w, C, I?

4. Suppose in the market for loanable funds, the supply of resources that are saved is increasing in the interest rate. Why might this be? Does this model, where savings increases with the interest rate, and the base model discussed in class, where savings is independent of the interest rate, have the same predictions for the impact of an increase in government borrowing and spending?

5. Derive the steady-state condition in terms of the equilibrium capital stock per person, k∗, starting from the law of motion for total capital, in a Solow model with positive population growth.

6. Illustrate the effects of a large amount of foreign aid, in form of capital goods, on a poor country in the Solow framework.

7. Suppose households don’t save anything up to a certain level. Up to income level ys - call it subsistence income - savings = 0. For income above this level, households save fraction s of their income as usual. Plot the cost-of-capital curve and the savings curve. Explain how the dynamics of convergence work here - are they different than usual?

8. Numerically, solve for equilibrium in a Solow model with a production function Y = K0.3L0.7

and parameters s = 0.2, δ = 0.08, η = 0.02. Should public policy try to encourage more or less saving here? Why?

9. (bonus) Draw the function Y = F(K,L̄) in terms of Y and K, for some fixed L. Justify, in words, the curvature of the line. Draw a line reflecting the cost of renting capital at a constant rate R. Vary R and show how this implies a capital demand function for the individual firm.

10. (bonus) Consider the production function Y = 10K0.38L0.62. Production functions of the form Y = AKαL1−α are termed Cobb-Douglas style functions. Show that the labour share in this economy is 0.62 and the capital share is 0.38 for any (K,L) combination.