Consumer and Firm Behavior: The Work-Leisure Decision and Profit Maximization

1. Consumer and Firm Behavior: The Work-Leisure Decision and Profit Maximization • For static model- one time period • Simple representative agent models consist of 1. the representative consumer 2. the representative firm

2. Consumer behavior • Focus on how a consumer makes choices concerning the trade off between consuming and working • The consumer must work harder and will enjoying less leisure time • Focus on How a consumer’s work-leisure choice is affected by his/her preferences and by the constraints he/she faces? • Consumer wish to make himself as well off as possible given the constraint that he faces -

3. Firm • Focus on how the available technology for producing goods and the market environment influence the firm’s decision concerning how much labor to hire during the period. • Acts to maximize profits, given market prices and the available technology.

4. Representative Consumer • 2 goods that consumer desires1. physical gd/consumption gd (aggregation of all consumer gd in the economy- measured in Agg. Consumption) 2. Leisure – time spent not working in the market (should also include recreational activities, sleep and work at home) Assumption: all consumers in the economy are identical – meaning as if only 1 consumer in the model – single representative consumer)

5. Representative Consumer • Consumer’s preferences over consumption and leisure as represented by indifference curves. • Consumer’s budget constraint. • Consumer’s optimization problem: making his or herself as well off as possible given his or her budget constraint. • How does the consumer respond to: (i) an increase in non-wage income; (ii) an increase in the market real wage rate?

6. Representative Consumer’s Indifference Curves • An indifference curve slopes downward (more is preferred to less). • An indifference curve is convex (the consumer has a preference for diversity in his or her consumption bundle).

7. Representative Consumer’s Indifference Curves • Utility function- to capture the preferences U (C, L) • Represents how the consumer ranks different consumption bundles • Refer to particular combination of consumption and leisure

8. Figure 4.1 Indifference Curves • IC = connects a set of points - with these points representing consumption bundles among which the consumer is indifference • Since more is preferred to less - A is strictly preferred to B

9. Figure 4.2 Properties of Indifference Curves • IC has 2 key properties: • IC slopes downward • IC is convex, that is bowed in toward the origin • The slope of IC – negative of the marginal rate of substitution • The rate at which the consumer is willing to substitute leisure for consumption in as moving from TO b

10. Representative Consumer’s Budget constraint • Specify his constraint and objective to predict what he will do • We assume that the representative consumer behaves competitively • The consumer is a price taker • He treats market prices as being given andn acts as if his action have no effect on those prices

11. Representative Consumer’s Budget constraint • Other assumption • Consumer always refer to all consumer • No money in this economy (No government supplied currency to be used in exchange) • No banks through which people can conduct transactions • Only 2 goods: consumption & leisure • Any trade in this economy must involves exchange of labor time for consumption goods or vice versa

12. Equation 4.1: The consumer’s time constraint • Consumer is assumed to have h hours of time available- which can be allocated between leisure time, l, and time spent working (or labor supply) Ns

13. Labor time sold by the consumer in the labor market – at price w in term of consumption good • 1 unit of labor time exchange of w units of consumption good • W is the real wage (the wage rate of consumer in units of purchasing power) • If the consumer works Ns hours => then his real wage income = wNs (expressed in unit of the consumption good)

14. The consumer’s real disposable income = wage income + dividend – taxes Other source of income for the consumer • Profit distributed as dividend from firms • Π (qty. of profit, in real terms, that the consumer receive)

15. In the model; firms have to be owned by someone- must be the representative consumer • Any π earned by firms , therefore must be distributed to the representative consumer as income=> dividend • Π is the real dividend income

16. The consumer pays taxes to the government • Assume that the real quantity of taxes is a lump sum (amount of T) • A lump sum tax – is a tax that does not depend in any way on the actions of the economic agent who is being taxed.

17. Budget Constraint • Consumer receives and pays taxes in terms of consumption goods- and he decides how much to consume out of this disposable income • For one period economy – the consumer has no motive to save • Why?

18. Equation 4.2: The consumer’s budget constraint • Because: the consumer prefer more to less- therefore all disposable income is consumed real disposable income Expenditure on consumption good • Consumption is equal to total wage income, plus dividend income, minus taxes.

19. Equation 4.3: Budget constraint accounting for time constraint. implicit quantity of real disposable income the consumer has implicit Expenditure on the 2 good (C, l)

20. Figure 4.3 Representative Consumer’s Budget Constraint (T>π)

21. Consumer Optimization • Assume – consumer is rational (consumer knows his own preferences and budget constraint and can evaluate which feasible consumption bundle is best for him) • Optimal consumption bundle - The consumer chooses the consumption bundle - that is on his or her highest indifference curve, while satisfying his or her budget constraint.

22. Figure 4.5 Consumer Optimization The marginal rate of substitution of leisure for consumption equals the real wage.

23. The Representative Firm • Consumer and firm come together to exchange labor for consumption good • Representative consumer supplies labor and demand consumption good • Rep. firm demand labor and supply consumption good

24. The Representative Firm The Firm: • Own productive capital => plant and equipment • Then hire labor to produce consumption good • Production function => production technology available to each firm - which describe the technological possibilities for converting factor inputs into outputs

25. Equation 4.9: The Firm’s Production Function Output of consumption good Quantity of labor input measured as total his worked by employee of the firm Quantity of capital input in the production process Total productivity

26. Since one period model (static): • K is a fixed input to production • Nd is variable factor of production In SR: • firm cannot vary the quantity of plant and equipment (K) – but they have flexibility in hiring and laying off workers (Nd)

27. z = TFP • Captures the degree of sophistication of the production process • ↑ in z makes both factors of production (K, Nd) more productive • Given factors inputs – higher z implies that more output can be produced

28. Marginal product of production (MPN) The additional output that can be produced with one additional unit of that factor input (labor), holding constant the quantity of the other factor inputs (K* , N*)

29. 5 Properties of the Firm’s Production Function 1. Constant returns to scale. • Given any constant , x>0, the following relationship holds: zF(xK, xNd) = xzF(K,Nd) • If all factors inputs are changed by a factor x – then output changes by the same factor x • A small firm is just that as efficient as a large firm Given a CRT production function : • the economy behaves in exactly the same way if there were many small firms producing consumption good • if there were a few large firms, provided all firm behave competitively (price taker in product and factor market) • HOWEVER, in this model – we assume only one firm in the economy – which represent all firms (representative Firm)

30. 2. Output increases with increases in either the labor input (Nd) or the capital input (K). • MP for both labor and capital – should be positive • MPN>0 ; MPK >0 • Both upward sloping • More input yield more output

31. 3. The marginal product of labor decreases as the labor input increases. • Declining MPN is reflected in the concavity of the production function • The slope of prod. function – MPN↓ as Nd ↑

32. 3. The marginal product of capital decreases as the capital input increases. • Declining MPK is reflected in the concavity of the production function • The slope of prod. function – MPK↓ as K ↑

33. 5. The marginal product of labor increases as the quantity of the capital input increases • Adding more capital => ↑ the MPN for each quantity of labor

34. Total Factor Productivity Increases Increase in TFP • more output is produced given each quantity of the labor input (K fixed) • Shift upward production function • MPN↑ (slope) for each quantity of the labor input when z ↑

35. Profit Maximization The goal of firm to maximize its profits given by Y-wNd Y: total revenue that firm receives from selling is output wNd: total real cost of labor input or total real variable cost .

36. Profit Maximization • Firm’s problem is to choose Nd to maximize • Π = zF(K, Nd) – wNd • Π = total revenue-total cost • To maximize profit; firm chooses Nd=N* • => maximize Π = distance AB (also distance ED)

37. Profit Maximization • At the profit maximizing , quantity of labor, N* • the slope of total revenue function = slope of total variable cost function • Or slope of production function = real wages • Or marginal revenue = marginal cost • Thus , firm maximizes profit by setting the marginal product of labor equals the real wage • Or MPN = w