Economics · Unit 5
Production and Cost Analysis
Exam-focused notes for Production and Cost Analysis (Economics, ECO155): what the TU syllabus asks and how it has actually been tested, with 14 solved past questions from this unit.
What this unit covers
- Production function definition and features
- Cobb-Douglas production function
- Isoquants definition and properties
- Optimum employment of variable inputs
- Law of returns to scale
- Total fixed cost and total variable cost
- Average fixed cost, average variable cost, and average total cost
- Marginal cost calculation and relationships
- Cost schedule computations
Isoquants definition and properties
What is a production function? Discuss the properties of isoquants with a diagram. [5]
A production function is a mathematical relationship that describes the maximum output (Q) that can be produced from given quantities of inputs (factors of production) such as labor (L) and capital (K), using the best available technology. It is expressed a...
Full solved answer →Define isoquants. What are the properties of isoquants? Explain. [5]
An isoquant (or iso-product curve) is a curve that represents all possible combinations of two inputs (typically labour and capital) that yield the same level of output. In other words, it is a locus of points showing different input combinations that produ...
Full solved answer →What are the properties of Iso-quant? [5]
An iso-quant (or isoquant) is a curve representing all possible combinations of two inputs (labour and capital) that produce the same level of output. The key properties are: - Iso-quants slope downward from left to right - This reflects the inverse relatio...
Full solved answer →Cost schedule computations
Cost Analysis Question
Consider the following cost schedule:
| Output | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| TFC (Rs.) | 20 | 20 | 20 | 20 | 20 | 20 |
| TVC (Rs.) | 0 | 30 | 50 | 80 | 120 | 160 |
a) Calculate TC, AFC, AVC, AC, and MC.
b) Explain the relationship between AVC and MC. [5+0+0]
Output (Q) 0 1 2 3 4 5 --------------------- TFC (Rs.) 20 20 20 20 20 20 TVC (Rs.) 0 30 50 80 120 160 Formulas: $$TC = TFC + TVC, \quad AFC = \frac{TFC}{Q}, \quad AVC = \frac{TVC}{Q}, \quad AC = \frac{TC}{Q}, \quad MC = \frac{\Delta TC}{\Delta Q}$$ Q TFC TV...
Full solved answer →Cost Analysis Question
Consider the following cost schedule:
| Output (Q) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|---|
| Total Cost (TC) | 200 | 250 | 254 | 265 | 270 | 300 | 350 | 380 | 400 | 420 |
a. Compute TFC, AFC, AVC, AC and MC.
b. Show the relationship between AC and MC. [5+0]
Q 0 1 2 3 4 5 6 7 8 9 --------------------------------- TC 200 250 254 265 270 300 350 380 400 420 TFC = TC when Q = 0, since fixed cost does not vary with output. $$TFC = 200 \text{ (constant at all output levels)}$$ $$TVC = TC - TFC$$ Q TC TVC -----------...
Full solved answer →Cost Schedule Analysis
Consider the following cost schedule:
a) At TFC = 120, compute TC, AFC, AVC, and ATC.
| Output | TVC | TC | AFC | AVC | ATC |
|---|---|---|---|---|---|
| 0 | 0 | 120 | - | - | - |
| 1 | 50 | 170 | 120 | 50 | 170 |
| 2 | 90 | 210 | 60 | 45 | 105 |
| 3 | 120 | 240 | 40 | 40 | 80 |
| 4 | 140 | 260 | 30 | 35 | 65 |
| 5 | 175 | 295 | 24 | 35 | 59 |
| 6 | 230 | 350 | 20 | 38.33 | 58.33 |
| 7 | 310 | 430 | 17.14 | 44.29 | 61.43 |
b) Draw the graph of AFC, AVC, and ATC.
[Graph showing three curves:
- AFC (Average Fixed Cost): downward sloping hyperbola approaching zero
- AVC (Average Variable Cost): U-shaped curve with minimum around output 3-4
- ATC (Average Total Cost): U-shaped curve with minimum around output 5-6, always above AVC by the distance of AFC]
[5]
- TFC = 120 (constant across all output levels) - Output: 0, 1, 2, 3, 4, 5, 6, 7 - TVC: 0, 50, 90, 120, 140, 175, 230, 310 Formulas: - $TC = TFC + TVC$ - $AFC = TFC / Q$ - $AVC = TVC / Q$ - $ATC = TC / Q = AFC + AVC$ Computation table: Q TVC TC = 120+TVC AF...
Full solved answer →Cost Analysis Problem
Consider the following cost schedule:
| Output | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|---|
| Total Cost (TC) | 300 | 330 | 354 | 372 | 396 | 450 | 540 | 672 | 840 | 1080 |
Output (Q) 0 1 2 3 4 5 6 7 8 9 ------------------------------------------ Total Cost (TC) 300 330 354 372 396 450 540 672 840 1080 Step 1: Total Fixed Cost (TFC) TFC is the total cost at output $Q = 0$ (cost that does not vary with output). $$TFC = 300 \tex...
Full solved answer →Cost Schedule Calculations
Calculate TC, AFC, AVC, AC, and MC under the total fixed cost 100, from the following cost schedule.
| Output | TVC | TC | AFC | AVC | AC | MC |
|---|---|---|---|---|---|---|
| 0 | 0 | 100 | - | - | - | - |
| 1 | 10 | 110 | 100 | 10 | 110 | 10 |
| 2 | 18 | 118 | 50 | 9 | 59 | 8 |
| 3 | 24 | 124 | 33.33 | 8 | 41.33 | 6 |
| 4 | 32 | 132 | 25 | 8 | 33 | 8 |
| 5 | 50 | 150 | 20 | 10 | 30 | 18 |
| 6 | 80 | 180 | 16.67 | 13.33 | 30 | 30 |
| 7 | 124 | 224 | 14.29 | 17.71 | 32 | 44 |
| 8 | 180 | 280 | 12.5 | 22.5 | 35 | 56 |
| 9 | 260 | 360 | 11.11 | 28.89 | 40 | 80 |
Where:
- $TC = \text{TFC} + \text{TVC} = 100 + \text{TVC}$
- $AFC = \frac{\text{TFC}}{\text{Output}}$
- $AVC = \frac{\text{TVC}}{\text{Output}}$
- $AC = \frac{\text{TC}}{\text{Output}}$
- $MC = \frac{\Delta \text{TC}}{\Delta \text{Output}}$
[5]
- TFC = 100 - Output (Q): 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 - TVC: 0, 10, 18, 24, 32, 50, 80, 124, 180, 260 - $TC = TFC + TVC$ - $AFC = TFC / Q$ - $AVC = TVC / Q$ - $AC = TC / Q$ - $MC = \Delta TC / \Delta Q$ TC = TFC + TVC: - Q=0: 100+0 = 100 - Q=1: 100+10 = 11...
Full solved answer →Cost Analysis Problem
Consider the following cost schedule:
| Output | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|---|
| TFC | 200 | - | - | - | - | - | - | - | - |
| TVC | 0 | 20 | 36 | 48 | 64 | 100 | 160 | 248 | 360 |
a) Calculate $TC$, $AFC$, $AVC$, $AC$ and $MC$.
b) Derive $TFC$, $TVC$ and $TC$ curves. Explain their relationship. [5+0]
- TFC = 200 (fixed cost, constant at all output levels) - TVC by output: Output (Q) 0 1 2 3 4 5 6 7 8 ------------------------------ TVC 0 20 36 48 64 100 160 248 360 Formulas: - $TC = TFC + TVC$ - $AFC = TFC / Q$ - $AVC = TVC / Q$ - $AC = TC / Q = AFC + AV...
Full solved answer →Cost Analysis Problem
The cost and output of a firm is as below:
| Output (units) | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| TC (Rs.) | 150 | 300 | 420 | 600 | 790 | 1000 | 1260 |
From this information find out:
i. AFC of producing 3 units ii. AVC of producing 4 units iii. Least AC level of output iv. MC of producing 5 units v. TVC of producing 6 units
[5]
Output (units) 0 1 2 3 4 5 6 ------------------------ TC (Rs.) 150 300 420 600 790 1000 1260 Total Fixed Cost (TFC) = TC at output 0 = Rs. 150 (cost incurred even when output is zero) --- $$AFC = \frac{TFC}{Q} = \frac{150}{3} = \text{Rs. } 50$$ --- Step 1: ...
Full solved answer →Production function definition and features
Define production function. Explain the optimum employment of two variable inputs in production function.[10]
A production function is a mathematical relationship that expresses the physical output of a firm as a function of the quantities of inputs (factors of production) used in the production process. It can be expressed as: Q = f(L, K, M, ...) Where: - Q = Quan...
Full solved answer →Cobb-Douglas production function
Define production function. Discuss the various features of the Cobb-Douglas production function.[10]
A production function is a mathematical relationship that describes the maximum output (Q) that can be produced from a given set of inputs (factors of production) at a particular level of technology. It can be expressed as: Q = f(L, K, M, ...) Where: - Q = ...
Full solved answer →Optimum employment of variable inputs
Explain the condition for optimum employment of two variable inputs. [5]
The condition for optimum employment of two variable inputs is based on the principle of equimarginal returns (also called the law of equimarginal utility in production context). For two variable inputs (say X and Y), optimum employment occurs when: $$\frac...
Full solved answer →Law of returns to scale
Explain the law of returns to scale. [5]
The law of returns to scale describes the relationship between changes in all inputs (factors of production) and the resulting change in output. It examines what happens to output when a firm proportionally increases all its inputs by the same percentage. W...
Full solved answer →Make Unit 5 stick
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