Keep money and loanable-funds graphs separate

Keep money and loanable-funds graphs separate

Question and evidence

Do two interest-rate diagrams measure the same market?

In a fictional money-market graph, nominal interest i and money demand obey M=100−10i; supplied money is 60. In a separate loanable-funds graph, real interest r gives saving S=10+2r and borrowing demand I=30−2r. Both examples use abstract units.

This packet uses fictional data to isolate a mechanism. It is not an empirical estimate.

Mechanism and worked example

Money demand concerns desired liquid balances; loanable funds compares saving and financing demand. Their standard classroom axes and interest concepts differ. A central bank’s operating framework matters: scarce-reserve diagrams are not a complete account of systems using administered rates and ample reserves. Graph predictions are conditional models.

Money equilibrium 60=100−10i gives i=4. Raising supply to 70 gives i=3 under fixed demand. Loanable-funds equilibrium 10+2r=30−2r gives r=5 and quantity 20.

Complication

A student labels the money graph with real interest and the loanable-funds graph with money balances. A policy note assumes a reserve injection mechanically raises lending by a fixed multiple; that requires institutional assumptions absent here.

Your investigation

Draw both diagrams with units on each axis. Shift money supply in one and borrowing demand in the other; explain why the curves must not be copied between diagrams.

Revise your answer to “Do two interest-rate diagrams measure the same market?” using both source IDs. Separate the checked calculation from a judgment, and identify evidence that could reverse your judgment.

Vocabulary

Loanable funds: A model of saving supplied and funds demanded for borrowing at different real interest rates.

Assumption: A condition accepted for a model or argument; it needs justification before applying the result elsewhere.

Independent extension

Independently extend the investigation “Keep money and loanable-funds graphs separate” with a documented real dataset or scholarly source. Preserve definitions, recreate one calculation or evidence table, compare a rival explanation and report why the teaching example cannot establish the real-world conclusion.

Inspect a rate that does not clear the market

Compare a posted rate with clearing

Two separate fictional markets. Predict the imbalance at the selected rate before changing it. The rate selector inspects planned quantities; it does not simulate an institution imposing a rate or actual trade allocation.

Market modelMoney balances — nominal interestLoanable funds — real interest Schedule changeOriginal schedulesDemand increasesSupply increasesBoth increase equallyLarger demand increaseLarger supply increase Rate to inspect0%1%2%3%4%5%6%7%8%9%10%

Quantity is a stock of money balances in teaching units. Demand = 100 − 10i; supply = 60. The nominal rate i is in percentage points per year. Supply is fixed with respect to i by assumption.

Horizontal scale: 0–160 money-balance units. Changing markets changes units and scale; compare shifts within one model, not distances across the two models. The vertical rate scale stays 0–10%.

Solid curve: demand. Dashed curve: supply. Circle: clearing point. Squares and their connecting line: planned quantities at the inspected rate. At clearing the squares overlap. These are comparative schedules, not measured time paths.

Nominal rate 2%: demand 80.00, supply 60.00, demand minus supply 20.00. Clearing rate 4.00%, quantity 60.00.

Desired quantity exceeds supplied quantity; the model points toward a higher rate. No adjustment speed or actual transaction count is inferred.

Planned quantities at every supported rate

Rate (%)	Demand	Supply	Demand − supply
0	100	60	40
1	90	60	30
2	80	60	20
3	70	60	10
4	60	60	0
5	50	60	-10
6	40	60	-20
7	30	60	-30
8	20	60	-40
9	10	60	-50
10	0	60	-60

Restore interest-market comparison

Controls are temporary. Record the original and changed equations, axis meanings and equilibrium points in the notebook. A quantity shift is supplied as an assumption; this panel does not estimate its real-world cause.

Explain the money-balance gap

Choose the original money market and inspect 2%, then 6%. Calculate the quantity gap before reading the status. Holding the money stock fixed, how could attempted bond purchases or sales change bond prices and nominal yields? Do not claim that everyone can obtain more money balances merely by selling assets to one another.

Check nominal-rate adjustment

At 2%, desired balances are 80 and supplied balances 60, a shortfall of 20. People attempting to increase money holdings may offer bonds for sale. In the classroom adjustment story, downward pressure on existing bond prices raises yields, increasing the opportunity cost of holding money and reducing desired balances. The supply of money does not increase simply because one person sells a bond to another.

At 6%, desired balances are 40 against supply 60. Attempts to exchange unwanted money balances for bonds put upward pressure on bond prices and downward pressure on yields. At 4%, both quantities are 60. These are conditional price-adjustment arguments, not a simulation of transaction timing, central-bank reactions or an ample-reserves operating system.

Explain the financing gap

Switch to the original loanable-funds market. Inspect 3%, then 7%. Identify the rate as real and the quantity as a flow per year. Explain why “eight units of excess borrowing demand” is not a statement that eight units of physical currency are missing.

Check real-rate adjustment

At 3%, planned investment demand is 24 and saving supplied 16, leaving excess demand of eight. Under these schedules, a higher real rate reduces desired financing and raises saving supplied. At 7%, demand is 16 and supply 24, pointing toward a lower rate. At 5%, the flows match at twenty per year. The quantities are plans at a given rate; the exercise has not allocated actual loans or identified borrowers who qualify.

Shift a schedule, then test the explanation

Within each model, compare the original, demand-increase and supply-increase cases at their own clearing rates. Next compare all three “both increase” cases. Sketch old and new curves on the same axes for each comparison; the live graph shows only the currently selected case, so retain the original coordinates in your notebook.

In a money-balance model, a higher transactions price level or real income can increase desired nominal balances at a given rate. A stipulated stock increase changes the supply line. In a loanable-funds model, a change in desired saving or expected project returns can shift a schedule. Those are possible mechanisms; the numerical shifts here are supplied assumptions, not estimated effects of a particular policy.

Check single and simultaneous shifts

Money-market clearing pairs (rate, quantity) are original (4,60), demand only (6,60), supply only (2,80), both equally (4,80), larger demand increase (6,80), and larger supply increase (2,100).

Loanable-funds pairs are original (5,20), demand only (7,24), supply only (3,24), both equally (5,28), larger demand increase (7,32), and larger supply increase (3,32).

Both schedules moving right raises the clearing quantity in these cases, but the rate can rise, fall or stay the same depending on relative shifts. A statement that “both increased” is insufficient to choose the rate direction. Changing the rate along an unchanged schedule is a different operation from shifting that schedule.

Reconcile saving before drawing a financing graph

Use a separate fictional annual national-account ledger: income/output Y=1,000, consumption C=650, government purchases G=200 and taxes T=180. Assume no depreciation, transfers, net foreign income or measurement discrepancy. The units are credits per year; these are flows, not wealth balances.

Calculate private saving Y−T−C, public saving T−G and national saving as their sum. In this simplified closed economy, reconcile investment with national saving. Then hold Y, C and T fixed while raising G to 220, and rebuild the identity. Explain what a held-fixed accounting comparison can establish and what it cannot predict.

Check the closed-economy saving ledger

Private saving is 1,000−180−650=170. Public saving is 180−200=−20. National saving is 150, matching investment 150 in the closed-economy identity Y=C+I+G. With G=220, private saving remains 170, public saving becomes −40 and national saving becomes 130. Under these held-fixed values, investment must be 130 for the accounting identity to hold.

This is not proof that every extra twenty of government purchases reduces actual private investment by twenty. Income, consumption, taxes, external financing or other conditions can change. An identity reconciles the supplied records; a behavioral model is needed to predict responses.

Keep two graph conventions from counting one deficit twice

One convention plots private saving against private investment plus government borrowing. Another plots national saving, already reduced by a public deficit, against private investment. Both can represent the same simplified economy. Do not reduce supply for the deficit and also add the identical borrowing to demand within the same construction.

Using the original ledger, show 170 of private saving financing 150 of investment plus 20 of government borrowing. Then show 150 of national saving financing 150 of investment. Explain why these different horizontal quantities do not describe contradictory accounts. For a behavioral example, return to the crowding-out investigation and identify which convention its graph uses.

Add external financing without changing signs silently

Return G to 200 and keep Y=1,000, C=650 and T=180. Suppose investment is now 190. Calculate the required net capital inflow and net exports under the simplified assumptions above. Write the expenditure identity and saving identity side by side. Use “net capital inflow” to mean foreign financing of domestic investment minus domestic financing abroad.

Before opening the last check, solve the unfamiliar record Y=1,200, C=780, G=240, T=260, I=210. Label each entry, preserve the annual units and explain why an inflow is positive in the financing equation but net exports are negative here. Save the work before comparing with the public answer. This is transfer practice, not a secure independent assessment.

Check external financing and an unfamiliar ledger

National saving stays 150. Investment 190 requires net capital inflow 40. Net exports are −40: 1,000=650+190+200−40. Thus I=S+net capital inflow, while S−I=net exports under this simplified no-net-income/no-transfer setup. Do not apply that last equality unchanged to a fuller current account with additional income or transfer entries.

For the unfamiliar record Y=1,200, C=780, G=240, T=260 and I=210 under the same assumptions: Private saving is 160, public saving 20, national saving 180, net capital inflow 30 and net exports −30. Verify 1,200=780+210+240−30. A public surplus can coexist with net foreign financing when investment exceeds national saving.

The graph workbench does not determine inflation, expected inflation, default risk or a country’s actual investment response. Keep its nominal and real rates separate from the saving-account identity. Independent assessment still requires unfamiliar learner-produced graphs and an evidence-based explanation of which assumptions apply.