Question

Answer the questions below by explaining step by step
Activity 1.11

Zambia produces two consumer goods, beef and pork. Only labour is required to produce both goods, and the economy’s labour force is fixed at 100workers. The table below indicates the quantity of beef and pork that can be produced daily with various quantities of labour.

No. Of workers Production of beef No. Of workers Production of pork
0 0 0 0
20 10.0 20 150
40 20.0 40 250
60 25.0 60 325
80 27.5 80 375
100 30 100 400


(a) By graphing beef on the X-axis and Pork on the Y-axis, draw the production possibility frontier (PPF) for Zambia, assuming that labour is fully employed.

(b) i. What is the opportunity cost of producing the first 10 units of beef?

ii. What is the opportunity cost of producing the next 10 units of beef?

iii. What happens to the opportunity cost of beef as more is produced?

(c) Suppose the actual production for a given period was 20 units of beef and 250 units of pork. Is it possible to produce this combination? Explain. What conclusion can you make from this information?

(d) Suppose that a central planner in this economy calls for an output combination of beef = 30 and pork = 150. Is this attainable? Explain.

(e) New technology is developed to produce beef so that each worker can now produce double the daily amount of beef indicated in the table above. What happens to the PPF? Graph the new curve of PPF on the initial PPF.

Answer 1

Let's work through each part of the problem step by step.

### Part (a): Graphing the Production Possibility Frontier (PPF)

1. **Identify the Axes**:
- On the X-axis, we will plot the production of beef.
- On the Y-axis, we will plot the production of pork.

2. **Data Table**: Create a table using the provided data to identify the points for the PPF.

| Beef Production | Pork Production |
|------------------|----------------|
| 0 | 0 |
| 10.0 | 150 |
| 20.0 | 250 |
| 25.0 | 325 |
| 27.5 | 375 |
| 30.0 | 400 |

3. **Plot Points**: Plot the points from the above table on a graph.
- (0, 0)
- (10, 150)
- (20, 250)
- (25, 325)
- (27.5, 375)
- (30, 400)

4. **Draw the Curve**: Connect the plotted points with a curved line that represents the Production Possibility Frontier (PPF). The PPF should slope downwards, demonstrating the trade-off between beef and pork.

### Part (b): Opportunity Cost

**Opportunity Cost** is defined as the value of the next best alternative forgone when a choice is made.

#### (i) Opportunity Cost of Producing the First 10 Units of Beef
- To produce the first 10 units of beef (using 20 workers), the economy reduces pork production from 150 to 0.
- So, the opportunity cost of producing 10 units of beef is 150 units of pork.

#### (ii) Opportunity Cost of Producing the Next 10 Units of Beef
- For the next 10 units (from 20 to 30 units of beef) using 20 additional workers (from 20 to 40 workers), pork production reduces from 250 to 150.
- The opportunity cost is thus 100 units of pork (250 - 150).

#### (iii) Changes in Opportunity Cost
- As beef production increases, the opportunity cost of producing each additional unit of beef tends to increase. This is evident because as more labour is allocated to beef production, fewer resources are available for pork, leading to a greater loss in pork output for each unit of beef produced.

### Part (c): Evaluating Production Feasibility
- The given combination is 20 units of beef and 250 units of pork.
- From the table, we see that producing 20 units of beef requires 40 workers and corresponds to 250 units of pork.
- Since both values align with the production capability represented by the PPF, it is indeed possible to produce this combination.
- **Conclusion**: The economy is producing on the PPF, indicating that it is using all its resources efficiently.

### Part (d): Attainability of the Output Combination
- Output combination proposed: Beef = 30 units, Pork = 150 units.
- To produce 30 units of beef, the economy requires 100 workers (as seen in the table).
- This yields 400 units of pork if all workers produce pork instead.
- Since it is not possible to produce 150 units of pork while simultaneously producing 30 units of beef (the PPF only allows for 400 pork total when at maximum beef production), this combination is **not attainable**.
- **Conclusion**: This output combination lies outside the PPF, reflecting inefficiency or unattainability.

### Part (e): New Technology and Changes to the PPF
- The new technology doubles the amount of beef produced by each worker. Based on the original table, the updated beef production would be:

| Workers | Beef Production (new) |
|----------------|-------------------------|
| 0 | 0 |
| 20 | 20 |
| 40 | 40 |
| 60 | 50 |
| 80 | 55 |
| 100 | 60 |

- **Effect on PPF**: The PPF will shift upwards and to the right for beef production, as more beef can now be produced with the same amount of labour.
- **Graph the New PPF**: You would plot the new beef values against the previous pork values (remaining the same), including:
- (0, 0)
- (20, 150)
- (40, 250)
- (50, 325)
- (55, 375)
- (60, 400)

- This effectively illustrates an outward shift in the PPF, indicating overall increased production capability in the economy.

In summary, this step-by-step analysis allows us to understand the production possibilities of Zambia's economy and how changes in technology can affect its capability to produce goods.