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The problem presented is about determining and graphing **isocost lines** in economics, given different prices for labor and capital. Here's a step-by-step breakdown:

### Given:
- **Price of labor (w):** Rp 10,000 per unit
- **Price of capital (r):** Rp 2,500 per unit

### (a) **Equation for the isocost lines**:
An **isocost line** represents the combinations of labor (L) and capital (K) that result in the same total cost for a firm. The equation for the isocost line is:

\[
C = wL + rK
\]

Where:
- \( C \) is the total cost.
- \( w \) is the price of labor.
- \( r \) is the price of capital.
- \( L \) is the quantity of labor.
- \( K \) is the quantity of capital.

For the total costs given as Rp 200,000 and Rp 500,000, the equations will be:

1. For \( C = 200,000 \):
\[
200,000 = 10,000L + 2,500K
\]
2. For \( C = 500,000 \):
\[
500,000 = 10,000L + 2,500K
\]

### (b) **Graphing the isocost lines**:
To graph these lines, we rewrite the equations in terms of \( K \) (capital):

1. For \( C = 200,000 \):
\[
K = \frac{200,000 - 10,000L}{2,500}
\]
\[
K = 80 - 4L
\]

2. For \( C = 500,000 \):
\[
K = \frac{500,000 - 10,000L}{2,500}
\]
\[
K = 200 - 4L
\]

So, these are two linear equations that can be plotted on a graph, with labor (L) on the x-axis and capital (K) on the y-axis. The slope of both lines is \( -4 \), meaning the lines are parallel.

### (c) **New isocost line when labor price decreases**:
Now, the price of labor decreases from Rp 10,000 to Rp 8,000 per unit. The new isocost equation for a total cost \( C \), with \( C = 500,000 \), will be:

\[
500,000 = 8,000L + 2,500K
\]

Rewriting in terms of \( K \):

\[
K = \frac{500,000 - 8,000L}{2,500}
\]
\[
K = 200 - 3.2L
\]

This is the new isocost line. It has a slope of \( -3.2 \), meaning it's less steep than the previous lines.

#### Summary:
- For part (a), we derived two isocost equations for total costs of Rp 200,000 and Rp 500,000.
- For part (b), the isocost lines are plotted and are parallel.
- For part (c), the new isocost line after the decrease in labor price is less steep.

Would you like further details on any of the steps or help with the diagram?

### Relative Questions:
1. How does the slope of the isocost line affect a firm's choice of inputs (labor vs capital)?
2. What happens to the isocost line if both the price of labor and capital increase proportionally?
3. Can we derive the optimal combination of labor and capital given a specific production function?
4. How do isocost lines relate to isoquants in production theory?
5. What are the implications of a change in labor price on the firm's cost structure?

### Tip:
Always remember that the slope of the isocost line is equal to the ratio of the price of labor to the price of capital, i.e., \( -\frac{w}{r} \).

Misalkan harga per unit tenaga kerja adalah Rp 10.000,- dan harga per unit modal adalah Rp 2.500,-. Tentukanlah persamaan garis isocost jika biaya total perusahaan adalah Rp 200.000,- dan Rp 500.000,-. Gambarkanlah kedua garis isocost pada satu diagram. Jika harga tenaga kerja menurun dari Rp 10.000,- menjadi Rp 8.000,- per unit, tentukanlah garis isocost yang baru! Kemudian gambarkanlah pada diagram yang sama pada butir (b).

Learn how to derive isocost line equations given labor and capital prices in an economics problem. Understand the impact of changing labor costs on the isocost line and see how to graph them step by step.

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