Potential Questions for First Test AGEC 317 - OLS



AGEC 317

Exam 2

Spring 2003

Do your own work. You can use a calculator and your 8½ x 11 inch cheat sheets. No other books, papers, notes, etc. can be used. Use the points as a guide for your time. Cheating on this examination will result in the recommendation of an “F” for the class.

Short Answer - answer as concisely as possible - 5 points.

1. Explain what is meant by the dummy variable trap. What is the common procedure used to avoid the dummy variable trap?

2. What two criteria discussed in class must be met before the adjusted R2 from two are more equations can be compared?

3. Excluding a relevant variable from an estimated equation, does what to the biasness and efficiency of the OLS estimator?

4. To estimate a demand equation for orange juice, you have collected data on total demand for orange juice, price of orange juice concentrate, per capita income, and price of apple juice concentrate. Write the auxiliary equation (given in class) for testing for multicollinearity between the independent variables.

5. Why are the cost of outlays for college you paid the last three years irrelevant in your decision making as to whether to attend A&M next semester?

6. In maximizing utility subject to a budget constraint, the following condition was obtained from the first order conditions, [pic]; where MU is marginal utility, p is the price of the good, and f and e are subscribe for the two goods. Provide an economic interpretation of this condition.

7. Using homogeneity properties, calculate the returns-to-scale for the following production function, [pic], where x and y are inputs and q is output. Provide an economic interpretation of the returns-to-scale.

Longer Answer - use point totals for time allocation

15 points

8. Use the following demand curve to answer each questions, [pic], where qd is quantity demanded, I in income, and P is own price.

a) Provide two other variables you would consider important in estimating the demand equation.

b) Calculate the price elasticity of demand for the equation at an income at the current income of $2 and current price of $5.

c) If the firm wanted to increase quantity demanded, what would you suggest to management?

30 points

9. To answer the following questions, use the attached Excel printout.

The estimated model is [pic], where Q is widget output, C is capital and L is labor.

a) What is the interpretation of the coefficient associated with labor, [pic] in this model?

b) What is the null and alternative hypothesis associated with the F-statistic associated with this equation. At an α level of 0.05, do you reject or fail to reject the null hypothesis?

c) Graphically, illustrate what the meaning of the p-value associated with the t-statistic for the coefficient associated with capital, [pic]. At an α level of 0.05, do you reject or fail to reject the null hypothesis?

d) Mathematically, what are the marginal product and average product functions for capital?

e) What four assumptions are necessary to derive the OLS estimates for this equation?

f) Besides the assumptions necessary for the Gauss Markov Theorem to hold, what assumption(s) are necessary to conduct statistical tests on this equation?

10 points

10. For the production function given by [pic], where q is output and x is the input, find the profit maximizing level of input. Assume output price is $1.00 per unit of q and input price is $0.10 per unit of x.

Show ALL your work to get any credit.

Graphical Answers - 10 points. Answer either question 11 or 12, but not both questions. If you answer both questions, 5 points will be deducted from your final test score and only question 11 will be graded.

11. Graphically, derive a linear demand curve (recall, to derive an linear line only two points are needed) from utility maximization subject to a budget constraint. Be sure to label your each axis, each curve, and clearly show which curve is fixed and which is variable. Assume a two good economy.

12. Graphically, show the relationship between a 3-stage production function (stages of production) and marginal costs, average variable costs, and average fixed costs. Be sure to label each axis and each curve. Assume a two input production function, with one input fixed.

|SUMMARY OUTPUT | | | | | |

| | | | | | | |

|Regression Statistics | | | | | |

|Multiple R |0.973382 | | | | | |

|R Square |0.947472 | | | | | |

|Adjusted R Square |0.945851 | | | | | |

|Standard Error |4.635249 | | | | | |

|Observations |168 | | | | | |

| | | | | | | |

|ANOVA | | | | | | |

|  |df |SS |MS |F |Significance F | |

|Regression |5 |62781.91 |12556.38 |4.99919 |0.06111 | |

|Residual |162 |3480.657 |21.48553 | | | |

|Total |167 |66262.56 |  |  |  | |

| | | | | | | |

|  |Coefficients |Standard Error |t Stat |P-value |Lower 95% |Upper 95% |

|Intercept |20.06596 |2.106824 |9.524271 |2.36E-17 |15.90558 |24.22635 |

|capital |0.46851 |0.223342 |2.097725 |0.043441 |0.436925 |0.500095 |

|labor |0.295673 |0.215025 |1.37506 |0.171011 |-0.12894 |0.720287 |

|capital -squared |-0.00099 |4.43E-05 |-22.271 |3.56E-51 |-0.00107 |-0.0009 |

|labor- squared |-0.0134 |0.005735 |-2.33669 |0.020679 |-0.02472 |-0.00208 |

|capital*labor |0.000864 |0.000428 |2.019975 |0.045034 |1.94E-05 |0.001709 |

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