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Columbia. Microeconomic theory exam. Becker, 1965.


The following set of Gary Becker’s microeconomic theory examination questions (found in a folder in the Milton Friedman papers at the Hoover Archives) does not have an institution identification. According to the copy of Gary Becker’s c.v. buried in the website at the Institute of Labor Economics (IZA) in Bonn, Germany, we can be reasonably confident that this course was taught while Becker was still a professor at Columbia University. 


Final Examination
Prof. G. S. Becker
January, 1965

THREE HOURS—Persons whose native language is not English can have an additional 45 minutes.

  1. (40 points) Answer each of the following as true, false or uncertain and justify your answer in the space provided.
    1. Over time in the U.S. since 1929 output of the service industries rose at about the same rate as that of goods. Since the price of services rose at least as rapidly as that of goods, the income elasticity of demand for services would be greater than that for goods.
    2. A weighted average of all price elasticities must add up to one.
    3. Suppose the excise tax on bus travel was reduced and not on plane, train or other travel. This would reduce the use of buses if such travel was a sufficiently strong inferior good relative to other kinds of travel.
    4. The ability of firms of very different sizes to survive in an industry means that the long run marginal cost curve is horizontal over the range of firm sizes that survive.
    5. If an increase in the output of any firm lowered the marginal cost curves of other firms in the same industry (external economies) a competitive industry as a whole might show increasing returns; i.e., have a negatively inclined supply curve.
    6. Short run marginal costs can never be below long run marginal costs.
    7. Suppose that a competitive firm maximizes not income but its sales subject to the constraint that it does not make any losses. Then reduction in the demand for its product might not lead it to reduce output.
    8. Goods X and Y are either substitutes, complements, or independent if an increase in the amount of X either reduces, raises or leaves unchanged the marginal utility of Y.
    9. If the price of a good competitively produced was free to vary and yet did not change much between a seasonal low and a seasonal high in demand, this means that the industry’s long run marginal cost curve was very elastic.
    10. An ad valorem tax, with a tax rate proportional to producer’s price, on a competitive industry that yielded the same revenue at the initial output as a specific tax, fixed amount per unit, would reduce output less than the specific tax.


  1. (20 points) Treat charitable contributions as a commodity entering the utility functions or indifference curves systems of the contributor. Assume, as is largely true, that contributions can be deducted from income in arriving at taxable income. Assume a proportional tax rate equal to t.
    1. What would be the effect of an increase in the tax rate for any one person alone on his contributions? How does your analysis compare with the traditional analysis for commodities?
    2. Is he more likely to increase or decrease his contributions?
    3. Suppose now the tax rate increased for everyone. Would your answers to a. and b. be significantly different?


  1. (20 points) Suppose the traffic department would like to enforce parking regulations in an efficient way. Assume that each person has the choice of parking illegally or legally; the latter costs X dollars per “day” and the former, if one is caught, causes a fine equal to F dollars per time caught.
    1. Assume first that the sole aim of the traffic department is to discourage illegal parking at minimum cost. Assume also that all drivers simply try to maximize expected money income. How frequently should the traffic department inspect parking in order to achieve its aim?
    2. If all drivers maximized expected utility and had diminishing marginal utility of income, (but there is no utility or disutility from disobeying the law), how would this affect your answer? If they had increasing marginal utility of income?
    3. Suppose the traffic department received all the fines and desired just to maximize its expected income. How would your answer to 1. be affected?
    4. How does your answer to a. and c. depend on F, the size of the fine, and X, the cost of legal parking?


  1. (20 points) Suppose the earnings of military personnel were set below the price that would make the number of volunteers equal to the demand by the military, and that draft calls were sent out strictly at random to males aged 18-26 to bring the number entering up to demand


1. How would the composition of drafted personnel compare with those that would enter if military earnings were raised sufficiently to make the number of volunteers equal to demand?

2. How would the total tax burden and its distribution among the population compare?

b. Assume now that drafted personnel could buy a substitute or substitute for someone else (as during the Civil War) instead of entering as a draftee. Assuming the capital market for substitutes works well, in equilibrium

1. How would the composition of men entering and the tax burden compare with that under a drafted and a fully voluntary system?

2. What determines the price that substitutes can get?


Source: Hoover Institution Archives.  Milton Friedman Papers, Box 80, Folde.r “University of Chicago, Student doctoral thesis and papers”.

Image Source:  Gary S. Becker from University of Chicago Photographic Archive, apf7-00059, Special Collections Research Center, University of Chicago Library.

Irwin Collier

Posted by: Irwin Collier