Lent - Lecture 1 - Short-run Analysis: The Keynesian Cross

Question 1

Short-run fluctuations are often - but not always - linked to volatility in …?

Answer 1

linked to volatility in aggregate demand

Question 2

Explain briefly, in three steps, the classical model for aggregate supply and aggregate demand

Answer 2

• the economy has a given supply of capital and labour
• these come together in a production function determining (inelastic) aggregate supply (Ys)
• aggregate demand adjusts (through r) to ensure Yd = Ys
• essentially: factors of production –> output –> demand

Question 3

Explain briefly, in three steps, the Keynesian approach to macroeconomics (to aggregate supply and aggregate demand)

Answer 3

• in the very short-run, firms sell what is demanded
• production adjusts elastically to absorb demand changes
• this determines factor employment
• essentially: demand –> output –> factors of production

Question 4

The Keynesian cross studies the relationship between which two things?

Answer 4

planned expenditure and actual expenditure

Question 5

What letter is used to denote planned expenditure?

Answer 5

E

Question 6

In this simple start of this model, what is the equation for planned expenditure. Define what each letter means. (not in terms of functions)

Answer 6

• E = C + I + G
• C: aggregate consumption
• I: aggregate planned investment
• G: government final expenditure

Question 7

What is the consumption function at this stage. Decompose this function. Define each term.

Answer 7

• C = C(Y - T)
• treat C(Y - T) as linear
• C(Y - T) = C̅ + c(Y - T)
• c: the marginal propensity to consume, 0 < c < 1

Question 8

What do we say planned investment depends on. Give the function for planned investment. What is the gradient of this function?

Answer 8

• planned investment depends on the real interest rate: r
• I = I(r)
• I’(r) < 0

Question 9

How do we treat government expenditure in the equation for planned expenditure?

Answer 9

treat government expenditure as exogenous

Question 10

What is the equation for planned expenditure? (given in terms of functions)

Answer 10

E = C̅ + c(Y - T) + I(r) + G

Question 11

For a given r, what does the planned expenditure function look like?

Answer 11

given r, the planned expenditure function looks a lot like the consumption function

Question 12

What is the equation for actual expenditure, A, in terms of Y? Why is this?

Answer 12

• A = Y
• as we know from the GDP identity that expenditure = income = output

Question 13

For an arbitrary Y, there is no reason why A should equal E. How do we end up spending a different amount than we planned? How come planned expenditure doesn’t necessarily equal actual expenditure?

Answer 13

• inventories play a critical role in the argument
• production counts for GDP when it happens, not when the good is sold
• for national accounting, unsold products are ‘bought’ by the firm producing them
• the accumulation of inventories happens when actual expenditure exceeds planned
• similarly, the depletion of inventories happens when actual expenditure is less than planned

Question 14

What is Y* in reference to the Keynesian cross?

Answer 14

Y* is the (goods market) equilibrium, where actual and planned expenditure coincide

Question 15

Describe what happens when output is below Y*?

Answer 15

• E > A
• inventories fall, firms raise production

Question 16

Describe what happens when output is above Y* in the Keynesian Cross?

Answer 16

• E < A
• inventories accumulate, firms cut production

Question 17

Derive the Keynesian multiplier

Answer 17

• in equilibrium we have Y = A = E
• Y = C̅ + c(Y - T) + I(r) + G
• rearranging:
• Y = (1/(1-c))(C̅ - cT + I(r) + G)
• so for every unit increase in G (or C̅, or I(r), …), Y increases by (1/(1-c)) > 1
• this is the Keynesian multiplier (1/(1-c))

Question 18

Briefly explain why output rise by more than ΔG (when government spending increases)

Answer 18

• increased government spending raises output (Y) … and thus disposable income (Y - T)
• higher disposable income means more consumption
• total planned expenditure rises further because of this
• the cycle continues…

Question 19

Give 2 situations why the multiplier would become less than 1/(1-c)

Answer 19

• if there were leakages from the circular flow, this would lead to a lower multiplier
• suppose taxes were proportional to income: C = c(1 - t)Y
  - multiplier becomes 1/(1 - c(1-t)) < 1/(1-c)