## ECON2213 – Assignment #1

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 discussed in Ch.3, explain what would 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 xed capital stock, K, and xed labor force, L. Suppose an earthquake destroys a chunk of the stock stock. What happens to Y, r and w, C, I? 4. Suppose in the market for loanable funds, the supply of resources that is saved is increasing in the interest rate. Why might this be? Does this model, where savings increase with the interestlabor market and a perfect

Y . State any assumptions you make.

labor force, L. Suppose an earthquake destroys

Y ,r and w, C, I?

rate, and the basis model discussed in class, where savings are 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 e ects of a large amount of foreign aid, in the form of capital goods, on a poor

country in the Solow framework.

7. Suppose households do not 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 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?

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

and parameters s = 0: 2,? = 0:08,? = 0:02. Should public policy try to encourage more or less

saving here? Why?

9. (bonus) Draw the function Y = F (K;? L) in terms of Y and K, for some xed L. Justify,

in words, the curvature of the line. Draw a line re ecting the cost of renting capital at a constant

rate R. Vary R and show how this implies the capital demand function for the individual rm.

10. (bonus) Consider the production function Y = 10K0: 38L0: 62. Production functions of the

form Y = AK? L1? are termed Cobb-Douglas style functions. Show that the labor share in this

economy is 0.62 and the capital share is 0.38 for any (K,L) combination.