Review Session 1 Microeconomic and Econometric Tools

1. Review Session 1Microeconomic and Econometric Tools Catalina Martinez catalina.martinez@graduateinstitute.ch Office hours: Tuesdays 6-8pm Rigot 27 Economics and Development MDev 2012-2013 THE GRADUATE INSTITUTE | GENEVA

2. Agenda • Introduction • Math • Microeconomics • Consumer • Producer • Welfare • Econometrics • Regression • Significance • Example in Stata

3. Introduction • For many of you the economic way of thinking might be new and you might even have certain prejudices. • The purpose of the curse is not to make you agree with it. Instead, the idea is to give you the tools that you need to understand it and to be able to challenge it. • Learn the language and the main logic (Review Sessions). • Read seminal economic papers and understand their arguments (Lectures).

4. Introduction • In this session we will go over basic microeconomic and econometric concepts that you need for the first half of the classand in particular for the first paper. • The next sessions will focus more on the week’s topic and on your questions. We will also devote some time for preparing the midterm exam.

5. Introduction • These review session is based on the slides available online for the books by Nicholson (micro) and Wooldridge (econometrics). They are very useful and clear. The links are on the course webpage. • If you need additional info, on the course webpage (additional readings for week 2) you have some links to • Varian (microeconomic theory) • Bardhan and Udry (development microeconomics) • If you have any questions or are blocked, please do not hesitate to contact me or come to my office hours.

6. Math

7. Economic Models • Economics uses models. They are simple and abstract but they help us understand complex problems. • Key assumptions: • Optimization (rationality) • Consumers maximize utility • Firms maximize profits • Government maximize public welfare • Ceteris Paribus • focus on the effects of only a few forces at a time, assuming that everything else is constant

8. Functions and derivatives We need basically two concepts from math to solve economic models: • Function • Is a relation between variables • Derivative • Tells us how y reacts with respect to (marginal/small) changes in x. It is the slope of a function. • A

9. Example • Example: Profits depend on produced quantity.   = f(q) Quantity

10. 2 q2 Maximization • Firms want to maximize profits, so they try different values of q to see how profits change  *  = f(q) 1 If the derivative is positive the firm will continue increasing its production (q) The firm will stop when the marginal benefit from producing is equal to zero, i.e. when the derivative is zero. q q1 q*

11. Microeconomics

12. Micro vs. Macro-economics • What is Economics? • It deals with a basic human dilemma: Scarcity • Limited resources vs. unlimited wants • Needs vs. potentials • Micro: bottom-up (1st part of the course) • How do we make decisions to allocate scarce resources? • Consumers and Producers • Macro: top-down (2ndpart of the course) • How does the whole economy function?

13. The Market • A market is a social construct where people meet to trade goods or services. • It facilitates exchange and distribution of resources in the society • It allows any item to be priced • A market is competitive if there are no participants big enough to be able to set prices (market power) • Infinite participants (buyers and sellers) • Homogenous goods • No entry and exit costs • No transaction costs • Perfect information

14. Equilibrium QD = Qs S P* D Q* The Market Price Any other price will lead to inefficiencies (excess demand or supply) Quantity per period

15. The Consumer: Utility Function • Believe it or not…utility is a function that represents what makes us happy. It is a big but powerful simplification. • It can contain goods and money, but also leisure, and other more intangible but somehow measurable inputs, etc…x1, x2,…, xn • The marginal utility that we derive from a good is the utility that an extra unit of it gives us. It can be measured with derivatives too.

16. Preferred to x*, y* ? ? Worse than x*, y* Graphical representation • If , i.e. utility comes from the consumption of x and y, then we have: Quantity of y y* Quantity of x x*

17. At (x1, y1), the indifference curve is steeper. The person would be willing to give up more y to gain additional units of x At (x2, y2), the indifference curve is flatter. The person would be willing to give up less y to gain additional units of x Indifference Curves • For a given level of utility indifference curves offer a graphical representation. • They show how much of y we are willing to give up for an extra unit of x, keeping the same level of utility. Quantity of y y1 y2 U1 Quantity of x x1 x2

18. Marginal Rate of Substitution • The negative of the slope of the indifference curve at any point is called the marginal rate of substitution (MRS) Quantity of y y1 y2 U1 Quantity of x x1 x2

19. Increasing utility U3 U2 U1 Indifference Curve Map Quantity of y U1 < U2 < U3 Quantity of x

20. I can afford to choose only combinations of x and y in the shaded triangle, i.e. below the BC line. The slope of the BC line is the relative prices of x and y all income is spent on y all income is spent on x, The Budget Constraint • If my utility comes from x and y, then I will spend my income on those two goods: y x

21. The individual can do better than point A by reallocating his budget A The individual cannot have point C because income is not large enough C B U3 Point B is the point of utility maximization U2 U1 Utility Maximization • Utility is maximized where the indiference curve is tangent to the budget constraint, i.e. where they have the same slope. Quantity of y Quantity of x

22. First-Order Conditions for a Maximum s.t Quantity of y B U2 Quantity of x

23. Implications of First-Order Conditions • For any two goods, • This implies that at the optimal allocation of income

24. Expenditure level E2 provides just enough to reach U1 Expenditure level E3 will allow the individual to reach U1 but is not the minimal expenditure required to do so Expenditure level E1 is too small to achieve U1 Expenditure Minimization • The problem can be solved from the opposite point of view… Quantity of y U1 Quantity of x

25. The Firm: Production Function • The production function shows the combinations of inputs, such as capital (k) and labor (l), necessary to produce a good (technology). • The marginal productivity of a given input represents how much units of product can be achieved by increasing a unit of that input. It can also be calculated with a derivative. • The marginal productivity of capital is • The marginal productivity of labor is

26. Diminishing Marginal Productivity • The marginal productivity of an input depends on how much of that input is already in use • In general, we assume positive but diminishing marginal productivity, • Example: having one teaching assistant is useful, a second might help, but a third one will not have a lot of work… • The marginal productivity is a function of its own. Therefore, we can see if it is increasing or decreasing by taking derivatives again, i.e. by taking the second derivative of the production function.

27. If the production function is given by q = f(k,l) and all inputs are multiplied by the same positive constant (t >1), then Returns to Scale

28. An isoquant shows those combinations of k and l that can produce a given level of output (q0) • The slope of an isoquant shows the rate at which l can be substituted for k At (lA, kA), the isoquant is steeper. The firm would be willing to give up more K to gain additional units of l At (lB, kB), isoquantis flatter. The firm would be willing to give up less kto gain additional units of l A kA B kB lA lB Isoquant k per period q = 20 l per period

29. The negative of the slope of an isoquant is the technical rate of substitution, andshows the rate at which laborcan be substituted for capital A kA B kB lA lB Marginal Rate of Technical Substitution (RTS) k per period q = 20 l per period

30. Each isoquant represents a different level of output q = 30 q = 20 Isoquant Map k per period Increasing output q = 10 l per period

31. I can afford to choose only combinations Of land kin the shaded triangle. The slope of the cost function line is the relative prices of l and k All costs come from k All costs come from w The Cost Function • If I can produce using l and k, then my costs of productions will be the wages that I pay to my workers and and the rent that I pay for my capital: k l

32. First-Order Conditions for a Maximum s.t Quantity of k A Q=constant Quantity of l

33. Implications of First-Order Conditions • For any two inputs, • This implies that at the optimal allocation of expenditure

34. Expenditure level E2 provides just enough to reach Q1 Expenditure level E3 will allow the individual to reach Q1but is not the minimal expenditure required to do so Expenditure level E1 is too small to achieve Q1 Expenditure Minimization • The problem can be solved from the opposite point of view… Quantity of k Q1 Quantity of l

35. General Equilibrium • Assume : • There are only two goods, x and y • All individuals have identical preferences • Resources are limited (i.e. there is a fixed amount of k and l) Then we can know how does the production possibility frontier of the economy behave. • An Edgeworth box shows every possible way the existing k and l might be used to produce x and y • any point in the box represents a fully employed allocation of the available resources to x and y

36. Labor in y production Labor for x Labor for y Capital in y production Capital for y Total Capital  Capital for x Capital in x production Total Labor Labor in x production Edgeworth Box Diagram Oy A Ox

37. y1 y2 x4 Total Capital y3 x3 y4 x2 x1 Total Labor Edgeworth Box Diagram Introducing the isoquants from x and y perspective… Oy Ox

38. Total Capital  Edgeworth Box Diagram • Point A represents the input endowment (ex: one agent produces x and the other y, the agent producing x has more labor and the one producing y has more capital). • Point A is inefficient because, by moving along y1, we can increase xfrom x1 to x2 while holding yconstant. • Agents would have to trade in order to move to the efficient point. Oy y1 y2 x2  A x1 Ox Total Labor

39. y1 p4 y2 p3 x4 Total Capital y3 p2 x3 y4 p1 x2 x1 Total Labor Edgeworth Box Diagram • For this to happen we just have to have a market and an equilibrium price for x and y. Since all actors have the same information, they will have the same price and they will maximize their profits on the the same point. • The locus of efficient points is the contract line. Oy Ox

40. Production Possibility Frontier • The locus of efficient points shows the maximum output of y that can be produced for any level of x • we can use this information to construct a production possibility frontier • shows the alternative outputs of x and y that can be produced with the fixed capital and labor inputs that are employed efficiently

41. Production Possibility Frontier Quantity of y The negative of the slope of the production possibility frontier is the rate of product transformation (RPT) Ox p1 y4 p2 y3 p3 y2 p4 y1 Quantity of x x1 x2 x3 x4 Oy Note that if we stand in any point inside the PPF, we could be producing more with the resources we have, so there is an inefficiency.

42. UJ1 UJ2 US4 UJ3 Total Y US3 UJ4 US2 US1 Total X From consumers to society… OJ Individual J OS Individual S

43. Pareto Efficiency An allocation is Pareto efficient if it is not possible to make one person better off without making someone else worse off

44. UJ1 UJ2 US4 UJ3 Total Y US3 UJ4 US2 US1 Total X Edgeworth Box Diagram At each efficient point, the MRS(of y for x) is equal for the utility of both individuals (J and S) OJ Individual J OS Individual S

45. Efficiency • In a Pareto Efficient allocation all individuals have the same MRS. • Since they are all optimizing their utility, we know that • In a perfectly competitive economy, all individuals have access to the same prices. • Therefore, if there is perfect competition, there will be a Pareto Efficient allocation.

46. First Theorem of Welfare Economics Competitive equilibriums are Pareto Efficient

47. Laissez-Faire Policies • If markets are perfect, then there is no need for public intervention. • Indeed, government intervention may result in a loss of Pareto efficiency. • Nevertheless, they are not: • imperfect competition • externalities • public goods • imperfect information • …

48. UJ1 UJ2 US4 UJ3 Total Y US3 UJ4 US2 US1 Total X Distribution Even if each of these points is efficient, some are more fair than others… OJ Individual J OS Individual S

49. US4 US3 US2 A  US1 Any trade in this area is an improvement over A Distribution If the initial endowment of individuals is not a Pareto efficient solution, they can both improve through trade OJ UJ1 UJ2 UJ3 UJ4 OS

50. The Distributional Dilemma • If the initial endowments are skewed in favor of some economic actors, the Pareto efficient solutions will also tend to favor those actors • Even if this result is efficient, it is not equal • Redistribution will be needed to attain more equal results