Instructor: Akos Lada Mid-Career MPA
Harvard Kennedy School Summer Program 2014
Problem/Question of the Day
Distributed: 7/25/14
Due in Class: 7/28/14
Questions 4-6: OPTIONAL
This is a modeling exercise. As a result, I will not give you functions or exact numbers, but you should write your own model for the problem. No two models are going to be exactly the same. When you make your assumptions, state them clearly, and keep in mind that generality comes at the cost of tractability. The best model is the most general one that still allows us to solve it. Try to write your model down with parameters rather than concrete numbers (e.g. for a linear demand curve write q(p)=a-bp rather than q(p)=4-2p). Please write equations algebraically, but graphs probably also help.
You would like to write a model for the choice of a country on production and consumption. Assume the country has a limited number of resources it can devote to producing military equipment and non-military consumption goods. Assume that if the country has absolutely no military equipment then it will conquered (bad outcome), or if it has absolutely no non-military consumption goods, the population will starve (bad outcome again…).
1. Model the production possibilities of the country. How many inputs are there? What is the resource constraint(s)? What is the shape of the production possibilities frontier?
2. Now model the consumption choice of the country. Assume some utility function. Why did you choose this utility function? What shape do the indifference curves take?
3. Assuming autarky, graphically illustrate the optimal production and consumption choices of the country.
4. (OPTIONAL) Assuming autarky, derive algebraically the optimal production and consumption choices of the country.
5. (OPTIONAL) Assume a technology breakthrough occurs in the military industry. How does this breakthrough affect the production and the consumption of the two goods?
6. (OPTIONAL) Go back to the original model (i.e. before question 4). Assume the world has become more peaceful, thus neighboring countries have reduced the size of their militaries. Model one way of how this exogenous change affects the consumption and production choices of our country.