Every module before this one has told a story: how a Fed hike ripples through an African budget, why food and fuel dominate the CPI basket, how debt dynamics decide whether a sovereign restructures. Those narratives are correct, but they have been carrying formal models underneath the whole time without naming them. This module makes the skeletons explicit. Three workhorse frameworks — AD-AS, IS-MP, and Solow — are the machinery that generated the intuitions in the earlier modules. Learn them and you can derive the narrative rather than memorise it.
Why bother with the algebra
A model is a disciplined way of asking 'what moves, and in which direction, when one thing changes?' The narrative modules gave you the conclusions; the models let you re-derive them under new conditions the course never covered. When Nigeria unifies its FX window or Kenya's drought breaks, you want the framework, not a remembered anecdote.
AD-AS: the short run of output and prices
The aggregate-demand/aggregate-supply model plots the price level (or inflation) on the vertical axis against real output on the horizontal axis. Aggregate demand (AD) slopes down: higher prices erode real balances and, in the modern telling, provoke a central bank to raise real rates, both of which cut demand. Short-run aggregate supply (SRAS) slopes up: with sticky wages and prices, firms produce more when the price level rises relative to costs. Long-run aggregate supply (LRAS) is vertical at potential output — in the long run, output is set by technology, capital, and labour, not by the price level.
The textbook usually spends its time on demand shocks: a fiscal expansion or a consumption boom shifts AD right, raising both output and prices in the short run. That framing fits the United States. It fits Africa badly. The defining feature of African inflation, established in the inflation-dynamics module, is that it is overwhelmingly a supply-side phenomenon.
In Africa, the action is on the AS curve
A poor harvest, a fuel-price spike, or a currency depreciation that passes through to import prices at 30-60% all raise costs across the economy. In AD-AS terms these shift SRAS leftward: the price level rises while output falls. This is why African central banks so often face stagflationary trade-offs — prices up and growth down at the same time — that a pure demand-driven model would call impossible.
Contrast the two shocks. A leftward AD shift lowers prices and output together — a recession the central bank can fight by easing, with no dilemma. A leftward SRAS shift raises prices while lowering output — the central bank must choose whether to tighten (defending inflation, deepening the downturn) or accommodate (protecting output, risking un-anchored expectations). The second case is the African norm, and it is exactly the dilemma the monetary-policy module described the CBK facing after the shilling weakened.
- Demand shock (rare as the dominant African driver): AD shifts — price and output move the same direction — no policy dilemma.
- Supply shock (the African norm): SRAS shifts — price and output move opposite directions — a genuine tighten-or-accommodate dilemma.
- The long run: whatever the short-run path, output returns to the vertical LRAS at potential; only supply-side reform moves potential itself — which is where Solow, below, takes over.
Check your understanding
A drought and a fuel-import price spike hit an African economy in the same quarter. In the AD-AS diagram, what happens, and why is it the hard case for the central bank?
IS-MP: the modern IS-LM
The old IS-LM model assumed the central bank fixed the money supply and let the interest rate be determined by money demand (the LM curve). No modern central bank works that way — the CBK, SARB, and the Fed all set a policy interest rate directly and let the money stock adjust. The updated model replaces LM with MP, a monetary-policy curve: the central bank chooses the real interest rate, typically by following a rule.
The IS curve
The IS curve is the combination of the real interest rate and output at which the goods market clears — planned spending equals output. It slopes down: a higher real rate raises the cost of borrowing, cuts investment and interest-sensitive consumption, and so lowers equilibrium output. Fiscal expansion, a commodity-export boom, or a surge in remittances shifts IS to the right at any given rate.
The MP curve and the Taylor rule
Instead of a money-supply curve, the central bank sets the real rate according to a reaction function. The canonical form is Taylor's (1993) rule, which says the nominal policy rate responds to inflation and to the output gap:
Here i is the nominal policy rate the bank sets, r* is the long-run real (neutral) rate, π is current inflation, π* is the inflation target, and ỹ is the output gap (actual minus potential output, as a percent). The coefficients φ_π and φ_y are how aggressively the bank leans against inflation deviations and output deviations. Taylor's original values were φ_π = 0.5 and φ_y = 0.5. The crucial property, the 'Taylor principle', is that φ_π must exceed zero so that when inflation rises one point the nominal rate rises by more than one point (1 + φ_π), lifting the real rate and actually restraining demand. A bank that raises nominal rates by less than the rise in inflation is loosening in real terms.
Reading a rate decision as a rule
When you read a CBK MPC statement, you are effectively watching an implicit Taylor rule. 'Inflation is within target and the output gap is closing, so we hold' is φ_π and φ_y both being satisfied at the current rate. Deviations from the implied rule — holding when the rule says hike — are usually fiscal-dominance or FX-defence considerations the plain rule omits.
Combine IS and MP and you get short-run output. But the transmission from the policy rate to actual spending — the whole point of the MP curve — is precisely what the monetary-policy module warned is weak in Africa. Shallow financial systems, concentrated banks that under-pass rate changes, thin interbank markets, and a large informal sector that borrows outside the banking channel all flatten the effect of a rate move. In IS-MP language, moving the MP curve produces a smaller change in output than the same move would in a deep financial system: the IS curve is steeper in the relevant region and the rate change reaches fewer borrowers.
Check your understanding
A central bank targets 5% inflation with a neutral real rate r* = 2%. Inflation runs at 8% and the output gap is +1% (output 1% above potential). Using the Taylor rule i = r* + π + 0.5(π − π*) + 0.5·ỹ, what nominal policy rate does the rule prescribe?
Check your understanding
Why does the same 100 basis-point rise in the policy rate typically move output less in a shallow African financial system than in a deep one?
Solow: the long run and growth
AD-AS and IS-MP are short-run models — they take potential output as given. The Solow model asks what determines potential output itself, and why some economies are rich and others poor. It is the formal skeleton under the structural-transformation and growth narrative of the course.
The production function
Output depends on capital K, labour L, and total factor productivity (TFP) A, through a constant-returns production function, usually Cobb-Douglas:
Dividing through by L and writing lower-case letters for per-worker quantities (y = Y/L, k = K/L) gives output per worker as a function of capital per worker:
Because α < 1, capital per worker has diminishing returns: the first tractors and roads and power lines added to a capital-scarce economy raise output a lot; the thousandth adds little. This single property drives everything that follows, including convergence.
Capital accumulation and the steady state
Capital per worker rises with saving and investment and falls with depreciation and population growth. A fraction s of output is saved and invested; capital depreciates at rate δ; and the workforce grows at rate n, which dilutes capital across more workers. Capital per worker stops changing — the steady state — when investment per worker exactly offsets depreciation-plus-dilution:
The left side, s·f(k) = s·A·k^α, is the actual investment curve — concave, flattening as k grows because of diminishing returns. The right side, (n+δ)k, is the break-even line — a straight ray from the origin showing how much investment is needed just to keep k constant. They cross once (besides the origin) at k*, the steady-state capital per worker. Below k* investment exceeds break-even and capital deepens; above k* it falls short and capital shallows. The economy converges to k* from either side.
Solving s·A·k^α = (n+δ)k for the Cobb-Douglas case gives closed forms worth remembering:
What Solow says and does not say
Higher saving s or lower population growth n raises the steady-state level of income — but not its long-run growth rate. In the basic model, sustained growth in output per worker comes only from growth in A (technology/TFP). Capital accumulation alone runs into diminishing returns and stops. This is why the model directs your attention away from 'just invest more' and toward productivity and technology — the heart of the structural-transformation argument.
Convergence — and why African growth accounting disappoints
Because of diminishing returns, a capital-poor economy starting below its steady state should grow faster than a rich one near its own — the 'convergence' prediction. Capital-scarce African economies ought, on this logic, to be catching up rapidly. Many have not. Growth accounting decomposes measured growth into contributions from capital, labour, and a residual (TFP, the Solow residual):
When economists run this decomposition for much of Sub-Saharan Africa, two patterns recur. First, the TFP residual g_A is low or even negative for long stretches — output has grown mainly by adding inputs (more workers, some capital), not by using them more productively. Second, capital deepening g_K has often been weak or has failed to stick: capital-shallowing episodes, where k actually falls, occur during conflict, macro instability, or investment collapses. Low TFP plus fragile capital accumulation is why the convergence the model predicts has been slow or absent, and why raising A — through institutions, human capital, infrastructure that works, and moving labour out of low-productivity informal activity into higher-productivity tradables — is the structural-transformation agenda in Solow's own vocabulary.
Conditional, not absolute, convergence
Solow predicts convergence to each economy's own steady state, which depends on its s, n, and especially A. Two economies converge to the same income only if they share the same fundamentals. African economies with low A and high n have low steady states — they can be 'converged' to a poor equilibrium and stall there. Convergence is a promise about the path toward k*, not a guarantee of catching up to rich-country income.
Check your understanding
In the Solow model, a country raises its saving rate permanently from 15% to 25%. What does the basic model predict for the LONG-RUN growth rate of output per worker once the new steady state is reached?
Check your understanding
An economy has TFP A = 1, capital share α = 0.5, saving rate s = 0.2, population growth n = 0.02, and depreciation δ = 0.03. Using k* = (sA/(n+δ))^(1/(1−α)), what is steady-state capital per worker k*?
Exercise · try it first
Two economies share the same technology A = 1, capital share α = 1/3, and depreciation δ = 0.05. Economy X (a stable East African performer) saves s = 0.24 with population growth n = 0.01. Economy Y (a fragile, conflict-affected state) saves s = 0.09 with population growth n = 0.03. (1) Compute steady-state capital per worker k* and output per worker y* for each, using k* = (sA/(n+δ))^(1/(1−α)) and y* = A·k*^α. (2) Interpret the gap in Solow terms. (3) The convergence hypothesis says poor economies grow faster and catch up — does that apply between X and Y here? (4) Connect the result to the course's structural-transformation and capital-shallowing themes.
The skeletons under the narrative
Step back and the three models map cleanly onto the course. AD-AS is the formal frame for the inflation-dynamics module: supply shocks shifting SRAS, not demand shocks shifting AD, are why African inflation is stagflationary and why the central bank faces a dilemma rather than a free lunch. IS-MP is the frame for the monetary-policy module: a central bank setting the real rate by a Taylor-type rule, with transmission weakened by shallow finance, is exactly the CBK the course described reading its own MPC statements. Solow is the frame for structural transformation: potential output set by capital, labour, and above all TFP, with convergence conditional on fundamentals and African growth accounting flagging low TFP and fragile capital deepening. The narratives were never hand-waving; they were these models, spoken in prose. Now you can run them yourself.