# MGEB12H3 Lecture Notes - Advanced Vector Extensions

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The table below describes the total product of a firm. Fill in the missing values, a) - u), by calculating marginal product and average product.

1 | 2 | 3 | 4 |

Units of the variable resource (Capital) | Total Product (TP) | Marginal Product (MP) | Average Product (AP) |

0 | 0 | a | - |

1 | 1 | b | l |

2 | 3 | c | m |

3 | 6 | d | n |

4 | 10 | e | o |

5 | 15 | f | p |

6 | 18 | g | q |

7 | 20 | h | r |

8 | 19 | i | s |

9 | 17 | j | t |

10 | 13 | k |
u |

Refer to the table from above.

a. List the units of capital exhibit increasing marginal returns?

b. List the units of capital exhibit decreasing marginal returns?

c. List the units of capital exhibit negative marginal returns?

8. Describe how the total product and average product curves change as a firm moves from increasing to diminishing to negative marginal returns.

9. Does the law of diminishing returns mean that, as a firm hires additional workers, each of those workers is successively worse at doing their job? Why or why not?

TABLE 66Stock Prices and Consumer Prices | |||

CITY | |||

Y = Rate of Change, Stock Prices, Percent Per Year | |||

X = Rate of Change, Consumer Prices, Percent Per Year | |||

CITY | Y | X | |

A | 5 | 4.3 | |

B | 11.1 | 4.6 | |

C | 3.2 | 2.4 | |

D | 7.9 | 2.4 | |

E | 25.5 | 26.4 | |

F | 3.8 | 4.2 | |

G | 11.1 | 5.5 | |

H | 9.9 | 4.7 | |

I | 3.3 | 2.2 | |

J | 1.5 | 4 | |

K | 6.4 | 4 | |

L | 8.9 | 8.4 | |

M | 8.1 | 3.3 | |

N | 13.5 | 4.7 | |

O | 4.7 | 5.2 | |

P | 7.5 | 3.6 | |

Q | 4.73. | 6 | |

R | 8 | 4 | |

S | 7.5 | 3.9 | |

T | 9 | 2.1 |

Table 66 gives data on percent change per year stock prices (Y) and consumer prices (X) for a cross section of 20 cities.

********************* answer in "SAS format" please********************* (if possible)**

1) Plot the data in scattergram

2) Regress Y on X and examine the residuals from this regression. What do you observe?

3) Since the data for city(E) is unusual, repeat the regression in (2) dropping the data on city(E). Now examine the residuals from this regression. What do you observe?

4) If on the basis of the results in (2) you conclude that there was heteroscedasticity in the error variance but on the basis of the results in (3) you reverse your conclusion, what general conclusions do you draw?

State whether the following statements are true or false. Breifly justify your answer:

5) When autocorrelation is present, OLS estimators are biased as well as inefficient;

6) The R squared values of two models, one involving regression in the first-difference form and another in the level form, are not directly comparable.

7) In the presence of heterscedasticity the usual OLS method always overestimates the standard errors of estimators.

8) If a regression model is mis-specified (e.g., an important variable is ommitted), the OLS residuals will show a distinct pattern.