# Production and Costs

Business I · Microeconomics · https://tryals.app/learn/business-i/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 $MC = \Delta TC / \Delta Q$.

| Curve | Shape | Driven by |
| --- | --- | --- |
| $AFC$ | Always falling | Fixed cost spread over output |
| $AVC$ | U-shaped | Diminishing marginal product |
| $AC$ | U-shaped | Sum of $AFC + AVC$ |
| $MC$ | U-shaped | Cuts averages at their minima |

**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.

## Practice questions

5 of this lesson's 13 practice questions, with answers. The full set is in the app.

### 1. Average cost curves are U-shaped: falling, then rising. What turns the curve around?

A. The firm running out of customers at high output
B. Rising input prices as the firm buys more
C. Depreciation, which accelerates with use
D. Fixed costs spread, then diminishing returns take over

**Answer:** D. Fixed costs spread, then diminishing returns take over

**Why:** Two forces in opposition, one weakening and one strengthening. AC falls while MC is below it and rises once MC exceeds it, which is why MC cuts AC exactly at its minimum.

Page: https://tryals.app/practice/business-i/production-and-costs/average-cost-curves-are-u-shaped-falling-then-rising-what-turns

### 2. Diminishing marginal product of labour is often attributed to workers becoming tired. What is the actual reason in the model?

A. Workers coordinate less efficiently as the team grows
B. Capital is fixed, so each worker has less to work with
C. Later hires are less skilled than earlier ones
D. Wages rise as more workers are hired, which reduces net product

**Answer:** B. Capital is fixed, so each worker has less to work with

**Why:** Workers are identical by assumption, so the falling product must come from the fixed capital being shared ever more thinly, twenty cooks in one kitchen. Skill and fatigue are real effects and are not what the curve is drawing, which is why the phenomenon disappears in the long run when capital can expand too.

Page: https://tryals.app/practice/business-i/production-and-costs/diminishing-marginal-product-of-labour-is-often-attributed-to-workers

### 3. Which are true about the MC-AC relationship?

A. MC crosses AC at the minimum of AC
B. When MC < AC, average cost is falling
C. When MC > AC, average cost is rising
D. MC is always above AC

**Answer:** A. MC crosses AC at the minimum of AC; B. When MC < AC, average cost is falling; C. When MC > AC, average cost is rising

**Why:** MC pulls the average down when below it and pushes it up when above it, they must cross at the minimum. MC is not always above AC.

Page: https://tryals.app/practice/business-i/production-and-costs/which-are-true-about-the-mc-ac-relationship

### 4. A firm has $FC = 500$ and produces 50 units. **Estimate AFC.**

**Answer:** 10 (within ±1)

**Why:** $AFC = 500/50 = 10$. Simple division, fixed costs spread over 50 units.

Page: https://tryals.app/practice/business-i/production-and-costs/a-firm-has-fc-500-and-produces-50-units-estimate-afc

### 5. Order from shortest run to longest run.

**Answer:**

1. Very short run: all inputs fixed, only price adjusts
2. Short run: labour variable, capital fixed
3. Long run: all inputs variable
4. Very long run: technology changes

**Why:** Time horizon determines which inputs can adjust, from momentary (none) to secular (everything including technology).

Page: https://tryals.app/practice/business-i/production-and-costs/order-from-shortest-run-to-longest-run