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MACROECONOMICS I UPF 2007-2008

MACROECONOMICS I UPF 2007-2008. LECTURE SLIDES SET 2 Professor Antonio Ciccone. SAVINGS, INVESTMENT AND THE CREDIT MARKET EQUILIBRIUM— OR FROM THE RENTAL PRICE OF CAPITAL TO THE REAL INTEREST RATE. Investment and savings meet in the credit (also loan) market

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MACROECONOMICS I UPF 2007-2008

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  1. MACROECONOMICS IUPF 2007-2008 LECTURE SLIDES SET 2 Professor Antonio Ciccone UPF Macroeconomics I Slide SET 2

  2. SAVINGS, INVESTMENT AND THE CREDIT MARKET EQUILIBRIUM— • OR FROM THE RENTAL PRICE OF CAPITAL TO THE REAL INTEREST RATE • Investment and savings meet in the credit (also loan) market • Households may have a PREFERENCE to save for consumption tomorrow. • This is captured by the following extremely simple SAVINGS FUNCTION: (E19) Households simply save a constant fraction s of their total income Y (this includes labor and capital income). Savings are deposited in banks that use them to make loans to firms. Firms use credit to buy NEW machines. INVESTMENT refers to the total purchases of NEW MACHINES and ALSO TO THE VOLUME OF LOANS IN THE ECONOMY. Firms can therefore buy machines or instead rent them. This will give rise to the rent-or-buy decision which determines the real interest rate. UPF Macroeconomics I Slide SET 2

  3. FIGURE 7 HOUSEHOLDS (aggregate labor endowment L(t) plus property rights in firms; preferences for consumption today and savings) GOODS MARKET (consumption and investment goods) LABOR MARKET CREDIT/LOAN MARKET (credit/loans for interest) FIRMS (technology of production; capital owned at the beginning of the period K(t))). RENTAL MARKET FOR CAPITAL GOODS UPF Macroeconomics I Slide SET 2

  4. How firms finance purchase of new machinery • Loans: firms ask banks for loans and banks make these loans with the savings of households • Retained earnings: firms ask their owners whether they can retain some of their earnings in order to fund purchases of new machinery • Issues of new shares: they purchases new machines and issue property titles to the machines (shares) directly to households • In the Solow environment these ways of financing machinery are all EQUIVALENT. We can therefore just think of firms financing the purchase of new machinery by asking banks for loans. UPF Macroeconomics I Slide SET 2

  5. 2. The rent or buy decision • The user cost of capital definition in discrete time • Firm can demand credit/loans to purchase capital goods: • in principle, this gives them an alternative to the rental market for capital • instead of renting the capital good next year, for example, you could buy it on credit today, use it for one year and then sell it off. • The cost of doing so is the USER COST OF CAPITAL -higher real interest rate and depreciation rate increase user cost -high future price for capital goods relative to current price reduces user cost UPF Macroeconomics I Slide SET 2

  6. 2. The user cost in one-sector growth models (which includes, among many, the Solow model) Assume that consumption goods and investment goods can be produced with identical technologies. In this case, the price of the investment goods relative to the capital good is always unity. If investment goods were more expensive only investment goods would be produced by profit maximizing firms. And vice versa. (E21) UPF Macroeconomics I Slide SET 2

  7. 3. The credit/loan market equilibrium • The CREDIT/LOAN MARKET is in equilibrium at time t when: • SAVINGS(t)=INVESTMENT(t) • S(t)=I(t) • As we will see, the CREDIT/LOAN market is brought into equilibrium by adjustments of the REAL INTEREST RATE. • The rent or buy decision and the credit/loan market equilibrium: • firms can either buy capital goods today (invest) for future use, or go to the rental market for capital in the next period. • the cost of renting next period is the cost of buying the investment goods use it and resell what is left is UPF Macroeconomics I Slide SET 2

  8. We will now show that in a CREDIT MARKET EQUILIBRIUM where INVESTMENT=SAVINGS>0: (E22) PART 1 OF THE ARGUMENT: Can it be that and that, at the same time the credit market is in equilibrium? No: in this case no firm wants to invest and I<S. Given the expected rental cost of capital, firms find it cheaper to rent some of this existing capital rather than invest in new one. Hence, the savings of HH are greater than the investment (which is 0). This situation will be eliminated by a fall in the real interest rate. UPF Macroeconomics I Slide SET 2

  9. PART 2 OF THE ARGUMENT: Can it be that and that, at the same time the credit market is in equilibrium? No: in this case firms want infinite investment because they can earn a profit by buying capital today and rent it out tomorrow. Hence, the desired investment by firms will be greater than the desired savings by firms, I>S. Hence, for the credit market to be in equilibrium firms must be indifferent by buying today and expecting to rent next period UPF Macroeconomics I Slide SET 2

  10. Because the expected rental price of capital next period is equal to the expected equilibrium MPK, see the static equilibrium condition, we obtain: (E23) • in equilibrium firms invest to the point where the MPK is equal to the real interest rate plus depreciation • - the equilibrium real interest rate is equal to the net MPK of the capital a society has accumulate up to time t UPF Macroeconomics I Slide SET 2

  11. 3. Summarizing the credit market equilibrium (E24) (E25) The STATIC EQUILIBRIUM CONDITIONS, -in the LABOR MARKET and the RENTAL CAPITAL MARKET and -the CREDIT MARKET EQUILIBRIUM CONDITIONS  DYNAMIC GENERAL EQUILIBRIUM UPF Macroeconomics I Slide SET 2

  12. 4. The credit market equilibrium and the link between present and future (or the capital accumulation equation in equilibrium) As far as the economics of the Solow model are concerned we are done! -We know how to determine output at a given moment in time given L and K; we also how to obtain factor prices and the real interest rate. - Now we know how to determine tomorrow’s capital stock given today’s capital stock and employment: Depreciation (E26) Net Investment Gross Investment UPF Macroeconomics I Slide SET 2

  13. Making use of HH SAVINGS behavior in (E19) S(t)=sY(t) (E27) Making use of the fact that aggregate income=aggregate output: (E28) this is the EQUILIBRIUM CAPITAL ACCUMULATION EQUATION UPF Macroeconomics I Slide SET 2

  14. 6. THE DYNAMICS OF THE SOLOW MODEL 1. The dynamics of capital accumulation To solve the Solow model completely, we need to specify the evolution over time of some EXOGENOUS factors like EFFICIENCY A and LABOR SUPPLY L We will assume that labor supply grows at (exogenous) rate n: (E29) (E30) (E31) UPF Macroeconomics I Slide SET 2

  15. Similarly, we will assume that exogenous efficiency A we will assume growth at (exogenous) rate a: (E32) (E33) (E34) UPF Macroeconomics I Slide SET 2

  16. SUMMARIZING THE DYNAMIC EQUATIONS OF THE SOLOW MODEL (E35) (E36) (E37) Following all 3 (so-called state) variables separately over time is somewhat cumbersome and inconvenient. And WE DO NOT HAVE TO, because as we have seen many things depend on capital per efficiency worker, NOT separately on K, L, and A. UPF Macroeconomics I Slide SET 2

  17. More convenient to focus on the change over time of CAPITAL PER EFFICIENCY WORKER WHY? - determines output per efficiency worker through the production function in efficiency form - getting to the quantities we are interested in is simple (E38) (E39) (E40) UPF Macroeconomics I Slide SET 2

  18. From TIME CHANGES OF K,L,A to TIME CHANGES in capital per efficiency worker (E41) UPF Macroeconomics I Slide SET 2

  19. Using the equilibrium capital accumulation equation (E28): (E42) (E43) (E44) UPF Macroeconomics I Slide SET 2

  20. This equation gives us the change in as a function of the present Therefore, given a starting point , it allows to study the whole time path of SO NOW WE ARE DONE WITH THE “MECHANICAL” DYNAMIC ASPECTS OF THE SOLOW MODEL TOO. Now is the time to remember: What is it we want to know about? UPF Macroeconomics I Slide SET 2

  21. What we want to know: “INTERMEDIATE” QUESTIONS - Will capital per efficiency worker INCREASE or FALL over time? - Will capital per efficiency worker GROW FOREVER? - Will the GROWTH RATE of capital per efficiency worker INCREASE or DECREASE in time? “FINAL” QUESTIONS - What does this imply for INCOME, WAGES, and INTEREST RATES. The questions are most easily approached graphically. UPF Macroeconomics I Slide SET 2

  22. FIGURE 8a Following capital per efficiency worker in time: THE PRODUCTION FUNCTION 0 UPF Macroeconomics I Slide SET 2

  23. FIGURE 8b Following capital per efficiency worker in time: SAVINGS AND THEREFORE INVESTMENT 0 UPF Macroeconomics I Slide SET 2

  24. FIGURE 8c Following capital per efficiency worker in time: THE EFFECTIVE DEPRECIATION LINE 0 UPF Macroeconomics I Slide SET 2

  25. FIGURE 8d Following capital per efficiency worker in time: CAPITAL GROWTH 0 UPF Macroeconomics I Slide SET 2

  26. FIGURE 8e Following capital per efficiency worker in time: THE CAPITAL GROWTH ZONE 0 UPF Macroeconomics I Slide SET 2

  27. FIGURE 8f Following capital per efficiency worker in time: FALLING CAPITAL ZONE 0 UPF Macroeconomics I Slide SET 2

  28. FIGURE 8g Following capital per efficiency worker in time 0 UPF Macroeconomics I Slide SET 2

  29. Some important terminology - BALANCED GROWTH PATH (also called STEADY STATE sometimes) An equilibrium where all variables grow at constant rates (this growth rate can be 0) - GLOBALLY STABLE BGP A BGP is globally stable if the economy ends up in the BGP in the long run NO MATTER WHERE THE ECONOMY STARTS. - CONVERGENCE A somewhat fuzzy concept. Many people seem to say that there is convergence if the growth rate of income per capital decreases as the country grows richer. UPF Macroeconomics I Slide SET 2

  30. The growth rate of capital per efficiency worker over time (E45) (E46) UPF Macroeconomics I Slide SET 2

  31. MPK 0 UPF Macroeconomics I Slide SET 2

  32. 0 UPF Macroeconomics I Slide SET 2

  33. APK= AVERAGE PRODUCT OF CAPITAL 0 UPF Macroeconomics I Slide SET 2

  34. APK 0 UPF Macroeconomics I Slide SET 2

  35. The growth rate of capital per efficiency worker over time (E46) UPF Macroeconomics I Slide SET 2

  36. 0 UPF Macroeconomics I Slide SET 2

  37. 0 UPF Macroeconomics I Slide SET 2

  38. 0 UPF Macroeconomics I Slide SET 2

  39. 0 UPF Macroeconomics I Slide SET 2

  40. 0 UPF Macroeconomics I Slide SET 2

  41. We have therefore shown the three following results: - Result 1: Over time capital per efficiency worker tends to its balanced growth path value, which we have denoted by (as long as the initial capital stock is strictly positive) • - hence, the economy will end up at the same level of capital per efficiency worker, no matter what the initial values for A,K,L • - Result 2: The closer capital per efficiency worker to its BGP value, the lower its growth rate • in the absence of SHOCKS to preferences or technology, the GROWTH RATE of capital per efficiency workers is therefore falling over time • Result 3: In the balanced growth path, growth of capital per efficiency worker is ZERO UPF Macroeconomics I Slide SET 2

  42. FIGURE 11 RESULT 1: over time capital per efficiency worker tends to its balanced growth path value 0 Time t UPF Macroeconomics I Slide SET 2

  43. FIGURE 12RESULT 2 and 3: the closer capital per efficiency worker to its BGP value, the lower its growth rate; in the long-run the growth rate is ZERO 0 Time t UPF Macroeconomics I Slide SET 2

  44. 2. From capital accumulation to growth of output per worker The easiest way to make the link is to assume the production function takes the so-called Cobb-Douglas form (E47) where is the elasticity of output with respect to capital: (E48) or UPF Macroeconomics I Slide SET 2

  45. The Cobb-Douglas production function in efficiency unit form is (E49) or (E50) hence is also the elasticity of output per efficiency worker with respect to capital per efficiency worker. UPF Macroeconomics I Slide SET 2

  46. Growth in output per worker - ouput per worker is output per efficiency worker times efficiency (E51) - differentiating therefore yields (E51) UPF Macroeconomics I Slide SET 2

  47. FIGURE 13 Evolution of output per worker (on LN scale) 0 Time t UPF Macroeconomics I Slide SET 2

  48. FIGURE 14: growth of output per worker a 0 Time t UPF Macroeconomics I Slide SET 2

  49. 3. Real wage growth and changes in the real interest rate Again, the easiest case is to assume the production function takes the so-called Cobb-Douglas form - the real wage is (E53) (E54)  the real wage is simply A CONSTANT FRACTION of income per capita and real wage growth is EQUAL TO output per worker growth UPF Macroeconomics I Slide SET 2

  50. FIGURE 15a Evolution of REAL WAGE (on LN scale) 0 Time t UPF Macroeconomics I Slide SET 2

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