Production and Costs

Production in Short and Long Run

Production functions map inputs to output: $Q = f(K, L)$. The isoquant shows all input combinations producing the exact same output.

In the short run, capital is fixed. The total product curve $TP(L)$ shows output from labour alone. Marginal product $MP_L = \Delta Q / \Delta L$ eventually diminishes due to the law of diminishing returns.

In the long run, all inputs are variable. The isocost line $wL + rK = C$ acts as the budget constraint. Cost minimisation requires tangency: $MRTS = w/r$, where $MRTS = MP_L / MP_K$.

Returns to scale define output scaling:

• Constant: doubling inputs doubles output.
• Increasing: doubling inputs more than doubles output.
• Decreasing: doubling inputs less than doubles output.

Short-Run and Long-Run Costs

Short-run costs link via $TC = FC + VC(Q)$, $AC = TC/Q$, and $MC = \Delta TC / \Delta Q$.

Pitfall / Key Rule: $MC$ intersects $AC$ and $AVC$ at their minimum points. When marginal is below average, average falls; when above, it rises. Just like one bad exam drags down your GPA.

The long-run average cost (LRAC) curve is U-shaped due to economies of scale at low output, constant returns in the middle, and diseconomies at high output.