Production and Costs
Introductory Microeconomics • Chapter 3
Q1-5
Production Function Concepts
[Image of total, average, and marginal product curves]
- 1. Production Function: It is the technological relationship between physical inputs and physical output. $Q = f(L, K)$.
- 2. Total Product (TP): The total amount of output produced with a given amount of inputs.
- 3. Average Product (AP): Output per unit of variable input. $AP_L = \frac{TP}{L}$.
- 4. Marginal Product (MP): The change in output resulting from using one additional unit of variable input. $MP_L = \frac{\Delta TP}{\Delta L}$.
- 5. Relationship between MP and TP:
- When MP > 0, TP increases.
- When MP = 0, TP is at its maximum.
- When MP < 0, TP starts falling.
Q6
Short Run vs Long Run
| Short Run | Long Run |
|---|---|
| A period where at least one factor of production (e.g., Capital) is fixed. | A period where all factors of production are variable. |
| Output can be changed only by changing variable factors (Labour). | Output can be changed by changing the scale of operation (all factors). |
Q7-8
Laws of Production
- Law of Diminishing Marginal Product: As more units of a variable input are combined with a fixed input, the marginal product of the variable input eventually declines.
- Law of Variable Proportions: In the short run, as variable input increases, TP initially increases at an increasing rate, then at a decreasing rate, and finally falls.
Q9-11
Returns to Scale (Long Run)
If all inputs are increased by a proportion $t$:
- Constant Returns to Scale (CRS): Output increases exactly by $t$ times.
- Increasing Returns to Scale (IRS): Output increases by more than $t$ times.
- Decreasing Returns to Scale (DRS): Output increases by less than $t$ times.
Q12-14
Cost Concepts and Relationships
Total Cost (TC) = Total Fixed Cost (TFC) + Total Variable Cost (TVC)
Average Cost (AC) = Average Fixed Cost (AFC) + Average Variable Cost (AVC)
Average Cost (AC) = Average Fixed Cost (AFC) + Average Variable Cost (AVC)
- TFC: Costs that do not change with output (e.g., Rent).
- TVC: Costs that change with output (e.g., Raw materials).
- AFC: $TFC / Q$. It is a rectangular hyperbola (continuously falling).
- AVC: $TVC / Q$. U-shaped curve.
Q16-21
Shapes of Cost Curves
- AFC Curve: Rectangular Hyperbola. (As Q rises, AFC falls but never touches zero).
- SMC, AVC, SAC Curves: U-shaped due to the Law of Variable Proportions.
- Relationship: SMC cuts AVC and SAC at their respective minimum points.
- Long Run: LAC and LMC are also U-shaped (often flatter) due to Returns to Scale.
Q22
Calculate AP and MP from TP Schedule.
| L | TPL | APL (TP/L) | MPL ($\Delta$TP) |
|---|---|---|---|
| 0 | 0 | – | – |
| 1 | 15 | 15 | 15 |
| 2 | 35 | 17.5 | 20 |
| 3 | 50 | 16.67 | 15 |
| 4 | 40 | 10 | -10 |
| 5 | 48 | 9.6 | 8 |
Note: The drop in TP at L=4 and rise at L=5 is based on the provided numbers, though atypical for standard economic models.
Q23
Calculate TP and MP from AP Schedule.
| L | APL | TPL (AP $\times$ L) | MPL ($\Delta$TP) |
|---|---|---|---|
| 1 | 2 | 2 | 2 |
| 2 | 3 | 6 | 4 |
| 3 | 4 | 12 | 6 |
| 4 | 4.25 | 17 | 5 |
| 5 | 4 | 20 | 3 |
| 6 | 3.5 | 21 | 1 |
Q24
Calculate TP and AP from MP Schedule.
| L | MPL | TPL ($\Sigma$MP) | APL (TP/L) |
|---|---|---|---|
| 1 | 3 | 3 | 3 |
| 2 | 5 | 8 | 4 |
| 3 | 7 | 15 | 5 |
| 4 | 5 | 20 | 5 |
| 5 | 3 | 23 | 4.6 |
| 6 | 1 | 24 | 4 |
Q25
Calculate Cost Schedules (Given TC).
Step 1: Identify TFC. At $Q=0, TC=10$. Therefore, TFC = 10.
| Q | TC | TFC | TVC (TC-TFC) |
AFC (TFC/Q) | AVC (TVC/Q) |
SAC (TC/Q) | SMC ($\Delta$TC) |
|---|---|---|---|---|---|---|---|
| 0 | 10 | 10 | 0 | – | – | – | – |
| 1 | 30 | 10 | 20 | 10 | 20 | 30 | 20 |
| 2 | 45 | 10 | 35 | 5 | 17.5 | 22.5 | 15 |
| 3 | 55 | 10 | 45 | 3.33 | 15 | 18.33 | 10 |
| 4 | 70 | 10 | 60 | 2.5 | 15 | 17.5 | 15 |
| 5 | 90 | 10 | 80 | 2 | 16 | 18 | 20 |
| 6 | 120 | 10 | 110 | 1.67 | 18.33 | 20 | 30 |
Q26
Calculate Cost Schedules (Given TC and AFC at Q=4).
Step 1: Identify TFC. Given $AFC = 5$ at $Q=4$.
$TFC = AFC \times Q = 5 \times 4 = 20$. So, TFC = 20.
| Q | TC | TFC | TVC (TC-TFC) |
AFC (TFC/Q) | AVC (TVC/Q) |
SAC (TC/Q) | SMC ($\Delta$TC) |
|---|---|---|---|---|---|---|---|
| 1 | 50 | 20 | 30 | 20 | 30 | 50 | 30* |
| 2 | 65 | 20 | 45 | 10 | 22.5 | 32.5 | 15 |
| 3 | 75 | 20 | 55 | 6.67 | 18.33 | 25 | 10 |
| 4 | 95 | 20 | 75 | 5 | 18.75 | 23.75 | 20 |
| 5 | 130 | 20 | 110 | 4 | 22 | 26 | 35 |
| 6 | 185 | 20 | 165 | 3.33 | 27.5 | 30.83 | 55 |
*SMC at Q=1 assumes TC at Q=0 is TFC (20). So $50 – 20 = 30$.
Q28
Production Function: $Q = 5 L^{0.5} K^{0.5}$
Given: $L = 100, K = 100$.
$$Q = 5 (100)^{0.5} (100)^{0.5}$$
$$Q = 5 (10) (10)$$
$$Q = 500$$
Maximum Output = 500 units
Q29
Production Function: $Q = 2L^2 K^2$
Case 1: $L = 5, K = 2$
$$Q = 2 (5)^2 (2)^2$$
$$Q = 2 (25) (4)$$
$$Q = 200$$
Case 2: $L = 0, K = 10$
$$Q = 2 (0)^2 (10)^2$$
$$Q = 0$$
(Production is not possible with zero units of Labour).
Q30
Production Function: $Q = 5L + 2K$
Given: $L = 0, K = 10$.
$$Q = 5(0) + 2(10)$$
$$Q = 0 + 20$$
$$Q = 20$$
Maximum Output = 20 units