Managerial Economics

First Midterm Examination

October 15, 1997

Mr. Upton

Directions: Each Problem has the indicated weight. Work all problems on the exam itself. I think I have left adequate space, but if necessary, use the back of the exam sheets, indicating that you have done so.

Name:

1. (10 Points). An increase in wealth means an increase in welfare. Explain whether you agree or disagree with this statement.

Disagree. This is a homework problem. An increase in wealth can lead to an increase in welfare, but need not. A reduction in interest rates will rotate the budget line, and, for a saver, lead to an increase in wealth and a decrease in welfare. I worked this in class.

2. (10 Points). It is a fact that East Waddle and West Waddle are initially alike. If a new technology is invented in East Waddle, then it will have a burst of saving and investment, guaranteeing it will thereafter always have a higher level of output per capita than West Waddle. Explain whether you agree or disagree with this statement.

Disagree. First, the increase in technology will give it a temporary advantage, for technology spreads. Second, the impact of a burst in saving will also be temorary without something else changing. Remember Winner/Loser/Neutral.

3. (20 points). A bright young MBA student who now has a lifetime utility function of the form

U = log(c₁)+ log (c₂) + log(c₃) +log(c₄)

expects to earn $200,000 in period 2, $300,000 in period 3 and then retire. The retirement decision is based on a promise by Aunt Sally to leave $200,000, which should come in period 4 of life. (You may assume that the MBA student firmly believes in Aunt Sally's promise). The discount rate is 100% per period.

1. Show how much the student will consume in each period of life. Explain your calculations.

Period	Consumption
1	50,000
2	100,000
3	200,000
4	400,000

The simple step is to recognize that initial wealth equals 200,000/2 + 300,000/4 + 200,000/8 = 200,000. Thus initial consumption is 50,000. The rest can be found either by working through the budget table or remembering the crescendo effect.

2. At the end of period 2, the MBA student is dismayed to discover that Aunt Sally has changed her mind and intends to endow a professorship in Economics instead. Show what consumption will look like over the life cycle.

Period	Consumption
1	50,000
2	100,000
3	150,000
4	300,000

The first two periods are clearly the same. In period 3 wealth would be 200,000 but the loss of Aunt Sally's money represents a reduction of 100,000 in wealth, or 50,000 in consumption. Thus consumption will be 150,000 in period 3 and 200,000 in period 4.

4. (40 points). Consider two countries, North Fuddle and South Fuddle, initially exactly like Neutral in all respects.

• South Fuddle has a volcano that has been dormant for 350 years. An investigation of this volcano, however, reveals beyond all doubt that it will erupt a year from now, (i.e., between year 1 and year 2) destroying 20% of the country's capital stock. It is physically impossible to move the capital stock, and the destruction is inevitable.
• By a cruel twist of irony, North Fuddle will benefit from the volcano. The volcanic ash is expected to enrich the soil of the country immediately after the eruption, thus boosting productivity. Thereafter, citizens in North Fuddle will represent 10% more effective labor units than their counterparts in South Fuddle and Neutral. (That is, each worker in North Fuddle will represent 10% more in year 2 a worker in South Fuddle or Neutral do in year 2, 10% more in year 3, etc. The idea is that while the number of effective labor units per worker will grow over time in each country, North Fuddle will have a 10% advantage each year, beginning in year 2 and thereafter.)

1. Compare wage rates, the capital rental rate, output per capita, the interest rate, and the saving rate in South Fuddle to those in Neutral in year 1.

Remember, output in year 1 is determined by population and capital stock. They are the same in North Fuddle, South Fuddle and Neutral. The volcano has yet to explode. Thus wage rates, capital rental rates and output per capita are the same in the 3 countries. The saving rate will fall since 20 percent of the capital will be wiped out by the impending disaster. The interest rate, next periods MPP of capital will rise, reflecting the lower capital labor ratio.

2. Compare wage rates, the capital rental rate, output per capita, the interest rate, and the saving rate in North Fuddle and Neutral in year 1.

Remember, output in year 1 is determined by population and capital stock. They are the same in North Fuddle, South Fuddle and Neutral. The volcano has yet to explode. Thus wage rates, capital rental rates and output per capita are the same in the 3 countries. The coming increase in the number of effective labor units will lower the capital/ELU ratio, and thus raise the interest rate. The higher interest rate will thus lower wealth, reduce consumption, and increase saving.

3. Compare wage rates, the interest rate, output per capita, the rate of growth, and the saving rate in South Fuddle to those in Neutral in steady state equilibrium.

This is Winner/Loser/Neutral all over again. The effects are transitory. Thus all variables will be the same in South Fuddle as in Neutral.

4. Compare wage rates, the interest rate, output per capita, the rate of growth, and the saving rate in North Fuddle and Neutral in steady state equilibrium.

ELU per worker will be 10% higher. But nothing else changes. Thus everything gets scaled up by 10%. The wage rate and output per ELU will be the same as in Neutral, but 10% higher per capita, given the higher number of ELU's per worker. The rate of growth, the saving rate, and the interest rate will be the same.