Topic 3- Consumption, Saving and Investment Flashcards
What is national desired consumption (C^d)?
The aggregate quantity of goods and services that households optimally consume, given income and other factors that determine economic opportunities
What is desired national saving (S^d)?
Level of aggregate saving when consumption is at its desired level
What is the formula for desired national saving (S^d)?
S^d = Y - C^d - G
What are the 2 periods of an individual’s consumption lifespan?
Current and future period
What is the budget constraint formula of the current period of an individual?
assets in the future period = current income + assets - current consumption
a^f = y + a - c
What is the budget constraint formula for the future period?
future period consumption = future period income + (1+real interest rate) x assets in the future period
c^f = y^f + (1+r)a^f
What is dissaving (|s|)?
Spending more than you have; c > y
When is an individual a borrower?
When: consumption > income + assets
c > y + a
When is an individual a lender?
When: consumption < income + assets
What is the trade-off between current and future consumption?
1 dollar of current consumption is traded for 1+r dollars of future consumption
By combining the current and future budget constraints, what is the overall budget constraint?
c + c^f/1+r = y + a + y^f/1+r
What is the utility maximisation problem for a household?
max U = u(c) + βu(c^f)
What does β represent?
Represents how the individual weighs current and future consumption. The more weight the individual places on future utility, the greater β is
What is the Euler equation/utility optimality condition?
u’(c) = β(1+r)u’(c^f)
What should the consumer do if the Euler equation does not hold true? i.e there’s an inequality
If the marginal utility of current consumption is greater than future consumption, the consumer should reduce future consumption and raise current consumption until they are indifferent
What is the consumption smoothing motive?
The desire to have a relatively even pattern of consumption
What is PVLR?
Present value of lifetime resources
What 3 changes does an increase in current income (y) provoke?
- Increase in PVLR
- The consumption smoothing motive dictates both current and future consumption increase
- Saving increases
What is marginal propensity to consume (mpc)?
The fraction of additional current income (y) that the individual allocates to current consumption (c)
What change does an increase in future income (y^f) provoke?
The same as an increase in current income except saving falls because current income remains constant
What does the Euler equation state?
That the individual must be indifferent between consuming one more unit today and saving that unit and consuming it in the future
What are the 2 main changes provoked by an increase in the real interest rate (r)?
- Substitution effect: current consumption (c) has become more expensive so falls whilst future consumption (c^f) and saving (s) rise
- Income effect: an increase in r implies an increase in wealth, hence a fall in c and c^f and a rise in s
What is the equation for expected real after-tax interest rate?
expected real after-tax interest rate = (1-tax rate)nominal interest rate - expected inflation
r^e_a-t = (1-t)i - π^e
What is the Ricardian equivalence proposition?
The idea that tax cuts do not affect consumption and do not affect national saving
What is the effect on tax on current desired consumption?
It’s ambiguous; it may either raise or lower current desired consumption
What are the 2 types of change in income?
- Temporary change: current income (y) changes while expected future income (y^f) is unchanged
- Permanent change: both current income (y) and future income (y^f) rise
What is the permanent income theory of consumption?
A permanent one-unit increase in income will raise current and future consumption more than a temporary one-unit increase will because it has a greater effect on PVLR
What is the Life-Cycle model?
Many period model which looks at patterns of income consumption and saving over an individual’s lifetime
What 2 main features does the Life-Cycle model show?
- Real income steadily rises overtime until near retirement, income drops sharply
- Saving is low or negative early in working life; max saving occurs when income is highest and dissaving occurs in retirement
What is the main assumption about fiscal policy?
That it does not affect aggregate supply
How does fiscal policy influence desired consumption (C^d)?
By affecting households’ current (Y) and expected future incomes (Y^f). The capital letters denote economy-wide levels
Give 2 ways in which fiscal policy affects desired national saving
- By affecting desired consumption (C^d), given the values of Y and G, a fall in C^d by $1 implies an increase of S^d by $1
- For any given values of Y and C^d, an increase in G will directly lower S^d
How do government purchases affect consumption?
Increases in G are financed by raising current taxes (T) so consumers’ after-tax incomes (Y_d) fall, hence consumption falls, though by less
What equation links the effect of a change in government purchases with desired consumption?
ΔC^d = mpc x ΔY_d = -mpc x ΔG
What is Investment?
The purchases or construction of capital goods
What is a firm’s desired (optimal) capital stock?
The amount of capital that allows the firm to earn the highest possible profit
What is the User cost of capital (uc)?
The sum of the interest cost, the depreciation cost and the capital loss
What is the equation for the User cost of capital (uc)?
User cost of capital = real interest ratexprice of capital goods + depreciation ratexprice of capital goods - change in the price of capital
uc = rp_k + dp_k - Δp_k
What is capital gain and how is it calculated?
The growth rate of the price of capital (Δp_k/p_k)
What is the condition determining a firm’s optimal amount of capital?
MPK^f = (r + d - Δp_k/p_k) x p_k
How does profit change with capital if MPK^f > uc?
Profit rises as K is added because marginal benefit exceeds marginal cost
How does profit change with capital if MPK^f < uc?
Profit rises as K is reduced because marginal benefit is below marginal cost
Where is expected profit maximised?
Where MPK^f = uc
What does the MPK^f curve show?
The value of the MPK^f for different sizes of K, given the size of the firm’s labour force and other factors of production
What 2 general factors cause the desired capital stock to change?
- Factors that shift the MPK^f curve
- Factors that change the user cost of capital
What 4 specific factors cause the desired capital stock to change?
- Change in real interest rate
- Changes in depreciation
- Changes in the price of capital goods
- Technological changes that affect MPK^f
What is the return to capital stock with taxes?
(1-t)MPK^f
where t is the tax rate on the firm’s revenue
How does a firm choose its desired stock?
A firm chooses its desired stock so that the return equals the user cost:
(1-t)MPK^f = uc
What is the expression for the tax-adjusted user cost of capital?
uc/1-t
Give 3 practical flaws with the way corporate taxes are looked at in these models
- We assumed that firm revenues are taxed when in reality profits are taxed
- Depreciation allowances reduce the amount of profit to be taxed
- Investment tax credits reduce taxes when firms make new investments
What is the effective tax rate?
The tax rate on firm revenue that would have the same effect on the desired capital stock as do the actual provisions of the tax code
What is the equation of the motion of capital?
K_t+1 - K_t = I_t - dK_t
What does the equation of the motion of capital state?
That net investment is equal to gross investment minus depreciation
How do firms optimally choose the level of capital stock for the next period?
I_t = K* - K_t + dK_t
where K* is desired capital stock
What is the expression for net investment?
K* - K_t
What are the 2 parts of gross investment?
- The firm’s desired net increase in K over period t
- The investment needed to replace worn-out capital
What are 3 factors that cause desired investment to fall and why?
- Increase in real interest rate (r): user cost increases reducing K*
- Increase in effective tax rate: tax-adjusted user cost increases which reduces K*
- Decrease in expected future MPK: K* decreases
What is the equation for aggregate quantity of goods and services supplied in a closed economy?
Y = AF(K,N)
What is the equation for demand on domestically produced goods (Y_ad)?
Y_ad = C^d + I^d + G
What is desired investment synonymous to?
Desired investment is synonymous to optimal or planned investment: I^d = I^p
What is the goods market equilibrium condition?
Y = Y_ad = C^d + I^d + G
What do firms do if aggregate demand turns out to be greater than aggregate supply?
Firms sell goods from their inventory stock
What is the goods market equilibrium condition?
Y - C^d - G = I^d = S^d
What shifts the saving curve to the right for any interest rate?
A change in the economy that raises desired national saving
Give 5 main factors that shift the saving curve to the right
- A rise in current output
- A fall in expected future output
- A fall in wealth
- A fall in government purchases
- A rise in taxes
What is the crowding-out effect?
Increased government purchases cause private investment to decline because the government is using more real resources
What shifts the investment curve to right at any interest rate?
A change in the economy that raises optimal private investment
Give 3 main factors that shift the investment curve to the right
- Any factor that leads to a fall in the user cost of capital (uc)
- A fall in the effective tax rate (t)
- A rise in the expected future MPK
