J. Wilson Mixon

The Solow Growth Model

The Solow growth model illustrates the long-run behavior of a macroeconomic system. Material on this Web site helps students understand this important model. The site’s primer makes the concepts accessible, and the Excel-based workbook lets students manipulate the model. The workbook follows Mankiw’s Macroeconomics, but it can be used as a stand-alone module. Students can easily find the steady state in Excel, and they can change parameters and variables to see how the system adjusts. Students also can consider the effects of various policy changes, especially those that affect the savings rate. If savings can be manipulated by policies, then analysts are faced with the normative issue of determining the “best” value of saving and, consequently, the “best” steady-state outcomes for capital, investment, and consumption. Also, students can use the workbook to see how changes in technology and population affect outcomes. The maximization of per-capita consumption is adopted as the Golden Rule Steady State. Students can see where this state occurs and can then easily change the savings rate to see how sensitive the steady state consumption rate is to these changes.

Lessons from the Specific Factors Model of International Trade

Abstract The Specific Factors model is an excellent learning tool. It provides insights into the meaning of economic efficiency, how complex economies simultaneously determine prices and quantities (and that it is relative prices that matter), and how changes in demand conditions or technology can affect income distributions among owners of factors of production. The authors develop this model using spreadsheets. Spreadsheets help students deal with “what-if” questions within prepared spreadsheets. They also give students the chance to look into the workings of the model and to change its structure. The exercise spreadsheets provide important advantages over using “black-box” presentations. Moreover, using spreadsheets gives students an opportunity to practice their use of spreadsheet software.

Cost Curves and How They Relate.

Despite decades of fine tuning, imprecision about long-run and short-run cost curves remains a source of confusion. This Web site contains Excel workbooks that draft consistent short-run and long-run cost curves and text describing these workbooks. The long-run curve is the proper envelope of the short-run curves, and all average and marginal curves are consistent. The workbooks can be used to develop instructional displays, handouts, and homework assignments letting students explore how changes affect output levels and profits. Drawing the marginal curve that corresponds to a nonlinear average curve can cause inconsistencies. The quantity at which marginal revenue curve intersects the improperly drawn marginal cost curve will not be the quantity at which profit (per-unit profit times quantity) is maximized. Equivalently, profit defined as per-unit profit times the number of units will not equal profit defined as the area between the marginal revenue and marginal cost curves. A graph in a leading principles textbook depicts the latter area as roughly 1.5 times the former area, a large enough discrepancy to confuse students. A common error in representing long-run versus short-run curves is to forget that where the average curves are tangent, the marginal curves must intersect. It is easy to overlook this necessary relationship in hand-drawing examples for the classroom or for examinations. Along with cost curves, the Web site presents revenues and profits for a price taker and a price maker.

Comparing trade instruments using spreadsheets

This article describes the use of Microsoft Excel to illustrate how different trade instruments affect total welfare. The article highlights seven Excel worksheets that show different trade instruments and their effect on total welfare. The first worksheet shows the determination of world equilibrium price and quantity for a two-country world example. A second shows how the imposition of a tariff affects the equilibrium price and quantity for both countries and the welfare of consumers and producers in both countries. A third shows how these same variables are affected if the country imposing the tariff is small relative to all other countries in the world. Another shows graphically how to measure consumer and producer surplus. The final three worksheets compare the effects of a tariff, a subsidy, and a support price on consumers’ and producers’ welfare and government revenue.

On the economics of tree farming and carbon storage

Abstract Popular wisdom advises cutting back on the use of wood products to ‘save trees’. This advice ignores the workings of markets and confuses the fundamental nature of forestry. As with most commodities, an increase in the demand brings forth an increased supply of wood and wood products. These products are largely from forests which resemble cropland much more than mines, so the increased flow of output corresponds to an increased stock of trees rather than depletion of a fixed stock.

Price discrimination and free-entry markets: the case of gasoline

S. Borenstein has demonstrated the compatibility of monopolistic competition and price discrimination. This paper applies this model to an industry that is often cited as the epitome of monopolistic competition, namely retail gasoline. It derives a hypothesis regarding the price spread between unleaded and leaded gasoline from a monopolistic competition model and tests that hypothesis. The empirical estimates are consistent with the models predictions.

Effects of U.S. affirmative action programs on women's employment☆

Abstract This study examines the impact that the equal employment opportunity (EEO) and affirmative action programs that were implemented in 1965 have had on the employment of women relative to that of men in the United States. Using time series data covering the period 1947–1988, the results indicate that women in the 20–54 age group benefited in terms of greater stability of employment (i.e., less sensitivity to short-run variations in employment) over the period 1965–1980, but they lost some of these gains over the period 1981–1988 (corresponding to the tenure of the Reagan Administration). Men in the same age group, on the other hand, experienced the opposite effect. That is, men in the 20–54 age group became more sensitive to short-run variations in employment over the period 1965–1980 and less sensitive over the period 1981–1988. The evidence also indicates that the EEO and affirmative action programs had the effect of increasing the share of projected employment of women in the 20–54 age group and in the 55–64 age group while decreasing the share of projected employment of men in the comparable age groups.

Nonlinearity and Chaos

One of the most exciting areas of current research in classical mechanics is the dynamic behavior of nonlinear systems. Nonlinear systems exhibit a much richer variety of behaviors than do linear systems. However, most nonlinear systems are impossible to solve using paper and pencil methods. It was only with the advent of digital computers that nonlinear dynamics really came into its own. With computer software like Maxima we can explore nonlinear dynamics in a way that is impossible without a computer.

Classical mechanics with Maxima

Introduction to Maxima.- Numerical Methods.- Newtons Laws of Motion.- Dynamics of Single Particles.- Oscillators.- Nonlinear Mechanics and Chaos.

Analyzing Subsidies in Microsoft Excel.

Applying the budget line/indifference curve apparatus to policy issues reveals important and sometimes counterintuitive policy implications. Also, it provides practice in using the apparatus. The author applies these tools to subsidies. The analysis follows textbook treatments but is extended at some points. In particular, the present analysis explicitly models consumer behavior when the consumer is also the taxpayer. The approach uses Microsoft Excel workbooks to depict a variable-quantity subsidy (housing) and a fixed-quantity subsidy (schooling). In each case, a Cobb-Douglas utility function represents consumer preferences. The budget sets reflect the policy being analyzed. With housing, the model shows the effect of providing a variable-quantity subsidy, including demonstrating that the consumer would prefer a lump-sum cash payment to a subsidy. It then removes the transfer effect by requiring that the consumer pay a tax equal to the subsidy. To do this the consumer must be simultaneously on the real budget line and on the apparent budget line created by subsidy. Excel shows students the nature of the constraints involved. Analyzing schooling shows that for three classes of consumers, a fixedquantity subsidy reduces schooling for two. Both types of consumers would choose more than the politically determined quantity. One type opts for the zeropriced, government-provided schooling. The other chooses to purchase schooling outside the government-operated system but buys less than before because paying for the government-operated schooling reduces income. The analysis also shows that a voucher program replicates the laissez-faire outcome for these two classes of consumers. For the third class, those who would buy less than the politically determined level, the voucher system yields the same quantity that the consumer would choose when schooling is offered free of charge.