Economics 102 Introductory Macroeconomics - Spring 2005 ...



Economics 102 Introductory Macroeconomics - Spring 2005, Professor J. Wissink

Problem Set 1 – ANSWERS

1.

a)

The Marginal Productivity of Labor (MPL) is defined as

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where the sign “(” denotes change (i.e. (y= y1-y0). Following this definition the Marginal Productivity of Labor in the production of Rafts and in the production of Girders is given by the following table

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b) The Law of Diminishing Returns does not apply in the production function of Rafts, because as labor increases the marginal productivity of labor stays constant. However, it does apply in the production of Girders. Diminishing returns “set in” after the 10th hour of labor, because the additional 10 hours of labor add less to the total output compared to the previous 10 hours.

c)

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d) The Production Possibilities Frontier (PPF) is generated by the following combination of output between rafts and girders.

e) The Total Opportunity Cost of 4 rafts is 19 girders (67-48). The Marginal Opportunity Cost of the 4th raft is 8 girders (i.e. (56-48)/(4-3)).

f) By looking at the graph you were given in the problem you cannot conclude that the Law of Diminishing Returns didn’t apply to the production of girders between 2000 and 2008. In order to test for the existence of Diminishing Returns you need to observe how output changes as labor changes, holding everything else constant. The graph below gives levels of output for different levels of labor used over the years, but technology was changing at the same time.

2.

| |Hours per Math exercise|Hours per |

| | |Econ exercise |

|Claire |0.5 |0.5 |

|Thomas |4 |1 |

a) Looking at MOCs, Claire’s MOC for each math problem is 1 econ problem while Tom’s MOC for each math problem is 4 econ problems, so Clair has the CA in math problems. Thomas has the CA in econ problems since he sacrifices only 1/4 of a math problem for each econ problem, where Claire’s MOC of an econ problem is 1 math problem.

b) Claire has the absolute advantage both in Math and Econ exercises. This is because she can write more exercises per hour than Thomas in each discipline.

c)

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d) (Note: there are various varieties of this same answer.) It is better for them to work together because Claire has a Comparative Advantage in Math and Thomas in Econ exercises. If each one of them is working separately 4 hours on each course then they can produce the following:

| |Math Exercises |Econ Exercises |

|Claire |8 |8 |

|Thomas |1 |4 |

|Total |9 |12 |

Consider now if they work together and Claire spends 5 hours doing Math exercises (she has CA in Math) and 3 hrs. doing Econ. Now let Thomas spend his 8 hours doing Econ exercises. The production of exercises will be

| |Math Exercises |Econ Exercises |

|Claire |10 |6 |

|Thomas |0 |8 |

|Total |10 |14 |

Clearly the total production of Math and Econ exercises increases by letting each one of them to specialize in the discipline in which they have a comparative advantage.

e) See graph.

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f) See graph.

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3.

a)

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b)

i) A devastating natural disaster unexpectedly hits the country flooding the corn plantations and killing thousands of people.

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Labor is reduced affecting the production of both goods, and also land is affected reducing the production of corn.

ii) The labor force grows over the next year due to lax immigration policy.

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iii) Workers in the car plants strike and instead go and work at the plantations.

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The PPF remains unaltered. The only thing that occurs is that the whole economy is producing at point A in the graph.

4. True or False and EXPLAIN: The law of diminishing returns implies that labor MUST be heterogeneous.

False. Labor could be identical, but when applied to a fixed factor of production, the marginal productivity of each unit of labor declines, because of the law of diminishing marginal productivity. It's because we have a fixed factor in the background in this case, and NOT because of any labor heterogeneity.

5. True or False and EXPLAIN: The law of diminishing returns implies that an input's marginal product must eventually be negative.

False. Negative marginal product indicates that labor is COUNTER productive - meaning that additional units of labor are DECREASING total output. The LDMR only says that in the presence of fixed inputs, at some point, we expect that increases in variable inputs will only INCREASE output at a DECREASING rate; so marginal product is getting smaller. It could get so bad that it is negative, but the law does not require that to be the case.

6. True or False and EXPLAIN: For a two country/two good world if Country A has the absolute advantage in both goods it must have the comparative advantage in both goods as well.

False. A can only have the comparative advantage in one good.

7. Multiple Choice:

1) (b)

2) (d)

3) (e)

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Corn

A

Automobiles

Corn

Automobiles

Corn

Automobiles

Corn

Automobiles

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