Producers — firms — convert inputs into outputs. The microeconomic question is: how much should they produce, with what input mix, and how do they respond to changes in input prices and output prices? The answers connect through the production function and the cost curves.
Production function
Production function
Q = f(K, L, M) • Q = output • K = capital input • L = labour input • M = materials/intermediate inputs (sometimes folded into K) The production function tells you the maximum output achievable from given input quantities. The 'maximum' assumption is technical efficiency — the firm uses inputs without waste. Marginal product of labour: MP_L = ∂Q/∂L. The extra output from one more unit of labour, holding capital fixed. Typically diminishes (each extra worker produces less than the previous) given capital is fixed. Marginal product of capital: MP_K = ∂Q/∂K. Symmetric.
Returns to scale
What happens to output when all inputs are scaled up proportionally?
- Constant returns to scale (CRS) — doubling all inputs doubles output. Many production processes approximate CRS over relevant ranges
- Increasing returns to scale (IRS) — doubling all inputs more than doubles output. Driven by indivisibilities, specialisation, network effects, large fixed costs spread over more units
- Decreasing returns to scale (DRS) — doubling all inputs less than doubles output. Coordination and management costs rise with size; communication breaks down
Returns to scale matter for market structure:
- CRS → competitive markets are sustainable with many firms
- IRS → natural monopoly tendency. Telecom networks, electricity transmission, large infrastructure
- DRS → small-firm equilibrium. Restaurants, retail, services with personal contact
Costs
Translating from inputs and prices to costs gives the cost curves.
Cost functions and curves
Total cost: TC = FC + VC • FC = fixed cost (doesn't vary with output) • VC = variable cost (varies with output) Average cost: AC = TC / Q Average variable cost: AVC = VC / Q Average fixed cost: AFC = FC / Q = AC − AVC Marginal cost: MC = dTC/dQ = dVC/dQ Key properties: • AFC falls monotonically as Q rises (fixed cost spread over more units) • MC and AVC typically rise as Q rises (diminishing marginal returns to variable inputs given fixed capital) • MC = AC at the minimum point of AC (the U-shape) • MC intersects AVC at AVC's minimum • Long-run cost curves are typically flatter (more inputs can be varied)
Profit maximisation
Firms maximise profit = TR − TC. The first-order condition:
Profit-maximising output
MR = MC Marginal revenue (the revenue from one more unit sold) equals marginal cost. For a perfectly competitive firm: MR = P (the firm sells at the market price, regardless of own quantity). So PROFIT-MAX OUTPUT is where P = MC. For a monopolist (or any firm with market power): MR < P (because to sell more, the firm must lower its price, which reduces revenue on all existing units sold). Profit-max output is where MR = MC, with P > MC at the optimum. The 'monopoly markup' is P − MC > 0.
Shutdown decisions
A firm should produce in the short run if: P ≥ AVC. Below this, even variable costs aren't being covered; the firm loses less by shutting down (losing only fixed costs) than by operating. In the long run, the firm exits if P < AC consistently.
The African small-firm productivity problem
Productivity (output per worker, or total factor productivity) varies enormously across African firms. World Bank Enterprise Survey data:
- Within-industry productivity dispersion is 5-10× higher in African economies than in OECD comparators. The top decile of firms within an industry is much more productive than the bottom decile
- Most economic activity is in tiny firms. Median firm size in Kenya is 1.5 workers; in Nigeria, ~2; in Ethiopia, ~3. OECD median is ~10
- Tiny firms have lower productivity per worker — typically 30-50% of the productivity of mid-sized firms in the same industry
- The 'missing middle' — the modest concentration of mid-sized firms (10-100 workers) that drive productivity in OECD economies is much thinner in Africa
Why the small-firm problem matters
Aggregate productivity reflects the WEIGHTED average of firm-level productivity. With most workers in small low-productivity firms, the aggregate is dragged down. Even if every firm became more productive, you'd need workers to MOVE FROM small to large firms for big aggregate gains. The causes of the small-firm trap: • Credit constraints — small firms can't borrow to expand because they lack collateral and credit history • Skills constraints — managing 50 workers requires different skills than managing 5. Few owners scale up • Regulatory transitions — moving from informal to formal status triggers compliance costs that small firms find prohibitive (Kenya's VAT threshold and the graduation cliff in Public Finance module 6) • Market thinness — small firms can serve nearby customers but extending reach requires logistics, branding, marketing investments • Risk-aversion — owners-managers of small firms are deeply risk-averse and don't bet on expansion that could fail
Returns to scale in African contexts
Many African industries have unfulfilled scale economies — the firms are smaller than the technology would support, leaving productivity on the table.
- Cement — heavy industry with substantial scale economies. East African Cement, Bamburi, Tororo Cement are mid-sized by global standards but reasonable by regional. New investment (Dangote Cement) at full scale
- Agro-processing — economies of scale in milling, oilseed crushing, dairy processing. African plants are usually sub-scale globally; entry of larger operations (Kenya's Brookside dairy, Bidco oils) has been productivity-positive
- Banking — IT scale economies, branch network economies, regulatory capital scale. The largest African banks (Standard Bank, First National Bank, Equity Bank) are sub-scale globally but increasingly competitive regionally
- Retail — global chains (Carrefour, Shoprite, Naivas) are scaling rapidly. Informal retail (kiosk-shop) loses market share over time as they scale up
Exercise
A Kenyan SME bakery currently produces 500 loaves of bread per day with 4 workers and 2 ovens. Fixed costs (oven depreciation, rent) are KES 5,000/day. Variable costs (flour, yeast, energy, labour) are KES 60/loaf. The retail price is KES 90/loaf. (1) Compute current daily profit. (2) Suppose the bakery is considering expanding to 1,500 loaves/day by adding ovens and 6 more workers. Variable costs rise to KES 65/loaf (some economies in input purchasing balanced by less-efficient operations at higher throughput), fixed costs rise to KES 9,000/day. Should they expand? (3) At what production level (with the new fixed and variable costs) would the bakery just break even? (4) What's the strategic reason an SME like this often doesn't expand even when the numbers say they should?