Microeconomics for International Trade Theory

1. Microeconomics for International Trade Theory ECON0301 January 2011

2. Basic Trade Model • General equilibrium • multiple agents (firms and consumers) all optimizing • The aggregation problem • One shot • long run • income=expenditure => balance of trade • Market structure • Constant returns to scale, perfect competition • Variable returns to scale, market power (new trade theory in 80s; new new trade theory in this past decade)

3. Basic Prerequisites • Consumption • Production • Perfectly Competitive Market • General Equilibrium

4. I: Consumption Theory

5. Consumption Problem • Consumption choice problem • Results: Demand functions • Equalization of marginal utility per dollar • Marginal rate of substitution = relative price

6. B A C Marginal rate of substitution = relative price At point A, the budget line and some IC are tangential to each other Omitting the negative signs, The slope of the IC = MUx/MUy The slope of the budget line = Px/Py

7. Y U1 U0 A C X Marginal rate of substitution = relative price At point C, MUx/MUy=Px/Py. But obviously not an optimal bundle Some properties on the shapes of ICs are required and will be assumed to hold.

8. Change in utility Along an IC The slope of an IC Marginal rate of substitution

9. Cobbs-Douglas Utility Function • CD utility function: • Marginal utilities: • MRS = relative price • Expenditure shares constant

10. Cobbs-Douglas Utility Function • Very nice demand functions • Without loss of generality, assume • If not, we can always represent the old CD utility function by a new CD function

11. V=2001 V=200 V=100 U=30 U=20 U=10 Measurability of Utility An order-preserving re-labeling of ICs does not alter the preference ordering.

12. Positive monotonic (order-preserving) transformation • They are called positive monotonic transformation • They all refer to the same preferences, leading to the same choice

13. Two properties of CD utility functions • Unit income elasticity • 1% increase in income => 1% increase in consumption • The aggregation problem • Given total income, income distribution does not affect market demand

14. The aggregation problem • Suppose there are N agents, each with the same CD utility function • Suppose their incomes are I1,I2, … , IN, summing up to I. • The total market demand for x equals • Given the total income, the income distribution among the agents does not affect the market demand. As long as the latter is concerned, we do not need to know income distribution. • A property need not generally hold for other utility functions

15. An example where income distribution matters • Two goods: necessity (x) and luxury (y) • Two agents, where I1+I2 = I = 10 • each will consume luxury only after x0 <5 units of necessity is consumed. • Suppose prices px=1, py=1. • Equal income, the market quantity demanded for x is 2x0; the market quantity demanded for y is 10 - 2x0 • Unequal income; suppose I1 < I2 and I1 < x0. Then market quantity demanded for x is I1 + x0 < 2x0; market quantity demanded for y is 10-(x0 + I1). • Unequal income diverts resource to luxuries while basic necessities are not fully provided => income distribution matters

16. The aggregation problem • The Cobb-Douglas utility function is among the family of utility functions for which income distribution per se does not affect market demand • We can further define the concept of “the relative demand for x” by an individual • This relative demand is independent of the individual’s income

17. The aggregation problem • The relative demand for x in the whole economy (with individual incomes I1, I2, …, IN) is just the same as the relative demand for x by any individual • Take out: With CD utility function, we can talk about • demand for x by the economy without knowing how income is distributed among individuals • Relative demand for x by the economy without knowing the total income

18. II. Production, Perfectly Competitive Market, Equilibrium

19. Production function

20. Production Function • Output elasticity and returns to scale

21. Production function • When returns to scale do not change with scale, for any t>1, the technology exhibits

22. Production function • For CRTS technology, there are two nice properties • MPK and MPL depend on K/L only, but not on the absolute scale • E.g., MPK the same when you hire K=3 and L=5, compared with when you hire K=6 and L=10. • MPK*K+MPL*L= f(K,L) • When factors are hired up to r = p*MPK and w = p*MPL, the profit is just zero!

23. Production function • We show the second property:

24. Profit maximization problem • Each firm chooses • If an optimum exists, will hire K and L such that

25. Cost minimization problem • Sometimes it is easier to re-phase the problem as a cost minimization problem, following by the output choice problem • Given input prices, choose the input combination that minimizes cost • Cost function

26. Cost function • When RTS does not change with scale, for any t>1, the technology exhibits

27. Isoquant – the locus of K and L such that the output level is constant Bending toward the origin K Optimal input mix to produce Q=10 Q=20 Iso-cost line Q=10 rK+wL=constant L isoquant

28. Main assumptions: CRTS technology, perfect competition, all inputs variable (long run equilibrium). The min. costs to produce $1 worth of a good are exactly $1. Given output and input prices, we can determine the optimal mix of inputs Or, given output price and K/L ratio, we can determine the relative input prices K Q=1/p’ Iso-cost line Q=1/p rK+wL=constant L Equilibrium condition

29. Equilibrium condition • For CRTS technology and in LR equilibrium, we cannot tell the output level of a particular firm, because every output level will lead to the same profit (which is zero) given fixed input and output prices

30. Cobb-Douglas Production Function

31. Cobb-Douglas Production Function • What does α+β=1 mean? • α+β>1; IRTS • α+β=1; CRTS • α+β<1; DRTS

32. The aggregation problem • Consider an industry with all firms having the same CRTS technology: Q=f(K,L); output & input markets perfectly competitive; and firms maximizing profits. Collectively, the industry employs K* and L*. • What is the total output of the industry? • f(K*,L*). The output produced would be the same as if there were one single firm employing K* and L*. The “fine structure” of the industry (i.e., the number of firms, the sizes, etc.) is irrelevant.

33. The aggregation problem • Let K1, K2, …, KN be the amount employed in the N firms. • Let L1, L2, …, LN be the amount employed in the N firms. • Cost minimization requires that K1/L1=K2/L2=… = KN/LN=K*/L*=a. • Total output

34. The aggregation problem • Question: What is the marginal product of capital (labor) in each firm? • Despite possibly different scales, each firm’s marginal product of capital is simply equal to ∂F(K*,L*)/∂K, i.e., marginal product of capital of a fictitious firm which employs just K* and L*. • Similarly, all firms have the same marginal product of labor = ∂F(K*,L*)/∂L.

35. The aggregation problem • Question: What is the rental rate of capital paid by each firm? What is the wage rate of labor paid by each firm? • Let P be the price of the good produced in the industry. The rental rate of capital is just P*∂F(K*,L*)/∂K, while the wage rate of labor is just P*∂F(K*,L*)/∂L. • The real rental rate (≡ w/p) and real wage rate (≡ r/p) should be ∂F(K*,L*)/∂K & ∂F(K*,L*)/∂L.

36. The aggregation problem • To know the output of an industry, as well the wage rate of labor and the rental rate of capital being paid by firms in the industry, there is no need to know the internal structure of the industry. • We can simply work out the problem by assuming all inputs (K* are L*) are hired by a single firm (which is nonetheless price taking in both input and output markets). • In this case, we can understand f(K,L) as an industry production function.

37. The aggregration problem • Takeout: given same CRTS technology, & LR competitive equil, the total K* and L* employed in the sector fully describe the output level as well as the real rental rate and real wage rate.