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CHAPTER 4

CHAPTER 4. Consumption, Saving and Investment. Desired Capital Stock. The amount of capital that allows the firm to earn the largest expected profit. To invest, benefits must > costs of using additional capital. Desired capital stock is when:

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CHAPTER 4

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  1. CHAPTER 4 Consumption, Saving and Investment

  2. Desired Capital Stock The amount of capital that allows the firm to earn the largest expected profit. To invest, benefits must > costs of using additional capital. Desired capital stock is when: MPKf = uc expected futuremarginal product of capital = expected user cost of capital uc = rpK + dpK = (r+d)pK expected real interest rate depreciation rate real price of capital goods

  3. User Cost of Capital pK = cost of capital goods = real price of capital goods i.e. buying a new oven at $100 measured in real dollars, pK=100 d = cost of depreciation = depreciation rate i.e. oven produces less 10% cookies after one year, d=0.1 r = cost of interest earnings sacrificed or interest payments paid = expected real interest rate i.e. government bond pays 8% interest rate = r=0.08 uc = interest cost + depreciation cost = rpK + dpK = 0.08(100) + 0.1(100) = 18

  4. MPKf vs uc MPKf At K = 4000, MPKf > uc. Increase K. uc At K = 5000, MPKf = uc. K*. uc At K = 4000, MPKf < uc. Decrease K. MPKf Desired capital stock is given by the intersection between MPKf and uc, where MPKf = uc. 4000 5000 6000 K

  5. Changes in uc MPKf uc decreased from uc1 to uc2 due to a decrease in real interest rate. (note: uc = rpK + dpK) At K = 5000, MPKf < uc. Increase K. At K = 6000, MPKf = uc. K*. ↓ r results in ↑ K uc uc1 uc2 MPKf 5000 6000 K

  6. Changes in MPKf MPKf MPKf increased from MPKf1 to MPKf2 due to an increase in technology. At K = 5000, MPKf < uc. Increase K. At K = 6000, MPKf = uc. K*. ↑ tech results in ↑ K uc uc MPKf2 MPKf1 5000 6000 K

  7. Taxes and Desired K At MPKf = 20, every additional K will increase revenue by $20. If tax = 20%, then firm pays extra $4 of tax from each additional $20 revenue, which gives firm after-tax additional revenue (or after-tax MPKf) equals to $16. Before tax = MPKf = 20. After tax (1-t)MPKf = (1-0.2)(20) = 16. To find K*, we must now consider MPKf=16 (after-tax). By formula … MPKf = uc (without tax) (1-t)MPKf = uc (with tax)

  8. Tax Impact on MPKf (1-t) MPKf = uc ↑t will ↓MPK thus ↓K An increase in tax rate, t, reduces the after-tax future marginal product of capital, reduces desired capital stock. MPKf uc uc MPKf1 MPKf2 (with tax) K2 K1 K

  9. Tax Impact on uc MPKf = uc / (1-t) ↑t will ↑uc thus ↓K An increase in tax rate, t, increases the tax-adjusted user cost of capital, reduces desired capital stock. MPKf uc uc1 Tax-adjusted user cost of capital = uc / (1-t) … shows how large before-tax MPKf must be if add one unit K. uc2 MPKf K2 K1 K

  10. Net Investment Gross investment (It) = total purchase or construction of new capital goods. Depreciation (dKt) = the amount of capital that wears out. Net investment (Kt+1 – Kt) = Gross investment (It) – Depreciation (dKt) Kt+1 – Kt = I - dKt I = Kt+1 – Kt + dKt I = K* – Kt + dKt Gross investment (I) Desired increase in capital (K* - K) Investment needed to replace depreciated K = +

  11. Desired Investment It = K* – Kt + dKt Any increase in K* will increase It Case 1: Real interest rate increases from 5% to 10%. Effect: uc = rpK + dpK increases, K decreases. r↑ K*↓ It↓ Case 2: Effective tax rate increases from 5% to 10%. Effect: tax-adjusted uc = uc/(1-t) increases, K decreases.t↑ K*↓ It↓ Case 3: Expected MPKf from 16 to 20. Effect: Intersection MPKf=uc moves upward. K increases. MPKf↑ K*↓ It↓

  12. End of Lecture 1 Week 5 • Desired Capital Stock • User Cost of Capital • MPKf versus uc • Changes in uc • Changes in MPKf • Tax Impact on MPKf • Tax Impact on uc • Net Investment • Desired Investment

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