# Exercises

*wxMaxima* Exercises to accompany *Microeconomic Theory and Computation*

Chapter 1

- The file 0101intro.wxmx contains a list of introductory exercises. In the first section, commands are entered and evaluated. The second section contains commands to bind expressions to names. In all workbooks, answers are provided in cells that have been closed. A line like this one identifies such cells : /*Input. Execute (ctrl-enter) for results */ … (4 lines hidden). Clicking on the black triangle at the left of the cell opens these cells. We recommend that you try to complete the exercises in each text cell before opening the input/output cell.

The workbook 0102Lists.wxmx, as its name indicates, contains exercises that involve creating and manipulating lists.

The workbook 0103Solutions.wxmx deals with solving equations and systems of equations. It contains a few graphs, but these cells are not hidden. A later workbook addresses graphing in more detail.

The workbook 0104manipulate.wxmx explores some of*Maxima*‘s ways of manipulating algebraic expressions.

The workbook 0105Calculus.wxmx introduces the elements of calculus-related topics: derivatives; integration, both analytical and numerical, and limits. It also addresses Taylor expansions and ordinary differential equations.

The workbook 0106draw.wxmx demonstrates features of draw2d( ) and draw3d( ).

Chapter 2

- The workbook 0201ProdPoss.wxmx involves a production possibilities frontier that consists of two linear segments.
- The workbook 0202DemSupp.wxmx reviews the basics of the competitive product market.
- The workbook 0203CompStat.wxmx looks at some comparative statics results and at elasticities.
- The workbook 0204CompStat2.wxmx also looks at some comparative statics results and at elasticities.
- The workbook 0205shifts.wxmx covers much the same ground as those above.
- The workbook 0206PriceFloor.wxmx examines two price-support programs.
- The workbook 0207Tax.wxmx extends the material in the text to address an ad valorem tax.
- The workbook 0208value.wxmx characterizes value and cost without identifying the units and, therefore, without explicit reference to markets. It illustrates the principle that the efficient quantity is the one at which marginal value and marginal cost (however they are measured) are equal to each other.
- The workbook 0209trade.wxmx considers the case in which domestic buyers are sellers are part of a world market, taking a world price as given. It begins with autarky, determining base values in the absence of trade. It considers the implications of having a world price above the autarkic price and below that price. Then it examines the economic effects of an import tariff.

Chapter 3. The workbook 03CobbDouglasUtility.wxmx reviews much of the material from the text, with the Cobb-Douglas utility function replacing the CES function.

Chapter 4

- The workbook 0401ThreeGoods.wxmx extends the CES utility function to include a third good. The exercises cover much of the material in the text, using this extended utility function.
- The workbook 0402Leisure.wxmx adds a time constraint. It begins with a choice of quantities of leisure and one other good. The last section extends the analysis to allow for two goods and leisure.

Chapter 5

- The workbook 0501QuasiLinear.wxmx develops a quasi-linear representation of utility and applies it to an
*ad valorem*subsidy. - The workbook 0502PriceIndices.wxmx applies the CES utility function to issues related to the construction of price indices.
- The workbook 0503Subsidy.wxmx examines the effect of an ad valorem subsidy such as an income tax exemption for mortgage interest payments.

Chapter 6. The workbook 0601CESproduction.wxmx reviews much of the chapter’s material with the CES production function, which exhibits uniform returns to scale (always decreasing, always constant, or always increasing) replacing the function in the text, which exhibits variable returns to scale.

Chapter 7

- The workbook 0701Nonhomogeneous.wxmx shows that, unlike their homogeneous counterparts, production functions that are not homogeneous can result in U-shaped long-run average cost curves.
- The workbook 0702CobbDouglas.wxmx shows that a homogeneous production function can result in a U-shaped long-run average cost curve if a minimum quantity of one input is required for production.

Chapter 8. No exercises

Chapter 9.

- The workbook 0901CobbDouglasSupply.wxmx is a short exercise in deriving a long-run supply curve. It is based on a slight generalization of the simple Cobb-Douglas production function.
- The workbook 0902ModifiedCobbDouglas.wxmx replicates its counterpart in Chapter 7 and adds exercises that explore the nature of industry supply.
- The workbook 0903Nonhomogeneous.wxmx reviews its counterpart in Chapter 7 and adds a few questions regarding supply.

Chapter 10

Chapter 11

- The file 1101ExportImport.wxmx is not a general equilibrium model, but it addresses international trade, a topic that the next three workbooks address using general equilibrium models.
- The file 1102Ricardian.wxmx contains exercises that involve the relatively simple Ricardian model of international trade, perhaps the simplest general equilibrium model.
- The file 1103SpecificFactors.wxmx extends the analysis to allow input substitution in each of two industries. In this model, one input, labor, is used in both industries. Each of the two other inputs, capital and land, is used in one industry but not the other.
- The file 1104Standard.wxmx develops the Heckscher-Ohlin model, which is a standard part of international trade theory.

Chapter 12

- The file 1201TariffQuota.wxmx reviews the case of imports in a price-taking industry. Then it shows how the results change. One of the differences is that quotas and tariffs have different implications for the domestic price even if the import level is the same under both.