Profit-Maximizing Behavior in Competitive Factor Markets
| English | Chinese | Pinyin |
|---|---|---|
| perfectly competitive factor market | 完全竞争要素市场 | wán quán jìng zhēng yào sù shì chǎng |
| wage taker | 工资接受者 | gōng zī jiē shòu zhě |
| cost-minimizing rule | 成本最小化法则 | chéng běn zuì xiǎo huà fǎ zé |
Hiring when you're one of many
- Imagine thousands of firms all hiring the same kind of worker.
- No single firm is big enough to change the going wage.
- Each simply pays the market wage and decides how many to hire.
- This is a perfectly competitive factor market 完全竞争要素市场.
A wage taker hires where MRP = W
- Each firm is a wage taker 工资接受者 — it can hire all it wants at the market wage.
- So its marginal factor cost is constant and equal to the wage, $W$.
- The hiring rule simplifies to $MRP = W$.
The labour market
In a competitive factor market the wage is set by market supply and demand; each firm takes that wage and hires where its MRP meets it.
A firm in a competitive factor market is a wage taker, so its marginal factor cost is:
It can hire any number at the market wage, so each extra worker costs exactly that wage.
In a competitive factor market the hiring rule simplifies to MRP = ______.
Since MFC equals the wage W, the firm hires where MRP = W.
A single wage-taking firm can lower the market wage by hiring fewer workers.
It is too small to affect the market wage — it simply takes the going wage.
The cost-minimizing rule
- When a firm uses several inputs, it should spend its budget so the last dollar on each brings the same extra output.
- The cost-minimizing rule 成本最小化法则: $\dfrac{MP_L}{P_L} = \dfrac{MP_K}{P_K}$.
- If one input gives more output per dollar, shift spending toward it until the ratios equalise.
The cost-minimizing combination of inputs sets:
Equalising MP/P across inputs means the last dollar buys the same extra output everywhere.
A worked case
- Labour costs 20 with a marginal product of 40, so $MP_L/P_L = 40/20 = 2$ units per dollar.
- Capital costs 10 with a marginal product of 30, so $MP_K/P_K = 30/10 = 3$ units per dollar.
- Capital gives more output per dollar, so use more capital and less labour until the ratios meet.
- That balance gives the chosen output at the lowest total cost.
Capital costs 10 with a marginal product of 30. What is its marginal product per dollar (MP/P)?
MP_K/P_K = 30/10 = 3 units per dollar — more than labour's 2, so use more capital.
Labour gives 2 units per dollar and capital gives 3. To cut costs, the firm should use:
Capital gives more output per dollar, so shift toward it until MP/P equalises.
In a perfectly competitive factor market each firm is a wage taker and hires where $MRP = W$. With several inputs, follow the cost-minimizing rule $\dfrac{MP_L}{P_L} = \dfrac{MP_K}{P_K}$ — shift toward whichever input gives more output per dollar.