Lecture 11. The Micro-founded AD–AS Model
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1. Overview
2. Microfoundations of the goods market
3. Microfoundations of the labor market
4. Equilibrium of aggregate demand and aggregate supply
5. Microfoundations of the money market
1. Overview
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⑴ Lucas critique (Lucas critique)
○ The marginal propensity to consume is not constant regardless of economic policy.
○ Temporary tax cut (e.g., a one-time lottery win) : c = 0
○ Permanent tax cut (e.g., winning the lottery every year) : c = 1
○ Not only the marginal propensity to consume, but also the coefficients of behavioral functions such as the consumption function and investment function can change with policy changes.
○ Because intuitive macroeconomic models have limitations, micro-founded macroeconomic models have emerged.
2. Microfoundations of the goods market
⑴ Consumption (C, consumption)
① Hypotheses about income
○ Hypothesis 1. Absolute income hypothesis : Keynes’s hypothesis that consumption is related only to the absolute level of current income.
○ Limitation : Even a temporary tax-rate cut changes current income, so it is viewed as having a large impact on changes in consumption.
○ Kuznets’s empirical analysis
○ Cross-sectional analysis : As the income level rises, APC decreases.
○ Short-run time-series analysis : In booms, APC is low; in recessions, APC is high.
○ Long-run time-series analysis : In the long run, APC is constant.
○ Keynes’s absolute income hypothesis cannot explain the long-run time-series analysis.
○ Hypothesis 2. Relative income hypothesis
○ Irreversibility of consumption : The marginal propensity to consume differs between decreases and increases in consumption; a ratchet effect appears.
○ Relativity of consumption : Also called the demonstration effect.
○ Hypothesis 3. Permanent income hypothesis (see below)
○ Hypothesis 4. Life-cycle hypothesis (see below)
② Formalization : Assume there are only period 1 and period 2.
○ Ci : consumer’s consumption in period i
○ Yi : consumer’s income in period i
○ Ti : lump-sum tax in period i
○ S : saving in period 1 (S ＞ 0) or borrowing (S ＜ 0)
○ a0 : initial assets
○ r : real interest rate on financial and real assets
○ U : a utility function with diminishing marginal utility; convexity with respect to the origin, i.e., preference for smoother consumption across periods
○ PV (present value) : the present value of lifetime consumption and also the present value of lifetime wealth; a constant
○ (Reference) Keynes viewed PV = Y1 − T1.
③ Generalization : Assume the substitution effect ＞ the income effect.
○ Endowment point (endowment) : the point (C1, C2) = (a0 + Y1 − T1, Y2 − T2), which the budget line always passes through even when the interest rate changes
○ case 1. An increase in the interest rate and a saver
○ Saver : a person who saves positively (S > 0); current consumption is lower than at the endowment point
○ Substitution effect : As the opportunity cost of current consumption rises, C1 decreases and C2 increases.
○ Income effect : As interest income rises, C1 and C2 increase (∵ assuming current and future consumption are normal goods)
○ If we assume the substitution effect ＞ the income effect, then C1 decreases.
○ case 2. An increase in the interest rate and a borrower
○ Borrower : a person who borrows (S < 0); current consumption is higher than at the endowment point
○ Substitution effect : As the opportunity cost of current consumption rises, C1 decreases and C2 increases.
○ Income effect : As interest costs rise, C1 and C2 decrease (∵ assuming current and future consumption are normal goods)
○ If we assume the substitution effect ＞ the income effect, then C1 decreases.
○ case 3. When current and future consumption are perfect complements : there is no substitution effect.
○ case 4. An increase in current income : the increase in current income ＞ the increase in current consumption
○ To smooth consumption across periods, saving in the present increases.
○ case 5. An increase in future income : the increase in future income ＞ the increase in future consumption
○ To smooth consumption across periods, borrowing in the present increases.
○ case 6. Current income and future income increase at the same time : the marginal propensity to consume approaches 1.
⑵ Investment (I, investment)
① Formalization : Assume there are only period 1 and period 2.
○ d : depreciation rate per unit of capital
○ I : total investment in period 1
○ Yi : output in period i
○ Ki : capital stock at the beginning of period i (initial capital stock is given as K1)
○ Li : labor input in period i
○ zi : total factor productivity or technology level at the beginning of period i
○ wi : wage in period i
○ F : a function increasing in capital and labor inputs; exhibits diminishing marginal productivity
○ (1-d) K2 : liquidation value of capital at the end of period 2; converted into consumption goods and sold in the goods market
② Generalization
○ Meaning of equation (#) : A firm’s optimal investment is determined by equating the marginal revenue of investment (left-hand side) with the marginal cost (right-hand side).
○ case 1. Real interest rate rises
○ Marginal cost of investment rises → investment demand falls → investment decreases
○ case 2. Depreciation rate rises
○ Direct effect : marginal return to investment falls → investment decreases
○ Indirect effect : period-2 capital stock falls → marginal product of capital in period 2 rises → investment increases
○ Generally, the direct effect is larger than the indirect effect → investment decreases
○ case 3. Total factor productivity rises
○ Marginal product of capital in period 2 rises → investment increases
⑶ Government spending (G)
① Formalization
○ B : government bonds issued only in period 1
○ Gi : government spending in period i
○ Ti : tax revenue in period i
② Key differences once the government budget constraint is included
○ Difference 1. The fiscal multiplier of government spending in the goods market changes (see below).
○ Difference 2. An increase in government spending changes not only the real aggregate demand curve but also the real aggregate supply curve (see below).
⑷ Aggregate demand and the real interest rate
① Aggregate demand in the period-1 goods market
② Applications
○ case 1. Real interest rate rises → C and I fall → Yd falls → movement along the IS curve (movement of a point)
○ case 2. Government spending rises → total expenditure rises → Yd rises → shift of the IS curve (the curve itself moves)
○ A permanent increase in government spending
○ A temporary increase in government spending : Because consumers smooth consumption across periods, part of the increase in government spending is absorbed into future consumption, so
3. Microfoundations of the labor market
⑴ Labor demand function
① Formalization : Assume there are only period 1 and period 2.
② Generalization
○ case 1. Period-1 real wage (w1) rises → labor demand falls → labor demand curve slopes downward (movement of a point)
○ case 2. Period-1 total factor productivity (z1) rises → period-1 marginal product of labor (MPL1) rises → labor demand falls (shift of the curve)
⑵ Labor supply function
① Formalization
○ U : increasing function; diminishing marginal utility
○ Ci : consumption in period i
○ li : leisure in period i
○ 1-li : labor supply in period i
○ wi : real wage in period i
○ Πi : firm’s profit in period i. Because shareholders are also workers, it must be considered.
② Generalization
○ When government spending changes, lifetime wealth PV changes, so labor supply changes.
○ Intuitive macroeconomic models do not consider the above mechanism.
⑶ Equilibrium in the labor market
4. Equilibrium of aggregate demand and aggregate supply
⑴ Formalization
5. Microfoundations of the money market
⑴ Overview
① Since the micro-founded AD–AS model is an extension of the classical model, the money market cannot affect the real sector.
② There are transaction media such as money and credit cards : “credit cards” include banks.
③ Because the money market offers no return but credit cards involve fees, there is an equilibrium between the two transaction media.
⑵ The credit card services market
Figure. 1. Credit card services market]
① Marginal benefit of credit card services = P(1 + R) : principal and interest obtained at the bank’s nominal interest rate
② Marginal cost of credit card services = P(1 + q) : the transaction amount (P) and the credit card service fee
③ Equilibrium in the credit card services market
⑶ The money market
① Xs(q) : supply of credit card services
② Xd(q) : demand for credit card services
③ X* : equilibrium transaction volume of credit card services
④ Y - X* : quantity of money held by consumers, firms, and the government
⑤ Md : nominal money demand; a decreasing function of the nominal interest rate
⑥ Ms : nominal money supply
⑦ V : income velocity of money; an increasing function of the nominal interest rate
⑧ Unlike the above model, Keynes viewed transaction money demand simply as an increasing function of income.
Entered: 2020.12.06 09:33