# I've been trying to find a solution to this without much success.

I am given the following....The production engineers at Impact Industries have derived the expansion path shown in the following figure. The price of labor is $100 per unit.

There is a graph showing the expansion path and three curves at 120, 180, 240 output levels.The expansion path hits these lines at(120) 20 (C)(capital units) 4(L)(Labor units, (180) 40 (C) 6(L), (240) 50(C) 8(L). There are three straight lines in faded gray that run with these curves...(120) 40(C) to 8(L), (180) 60(C) to 12(L), (240) 90 (C) to 18 (L)...I hope this helps recreate the graph? Capital runs by 10's to 100 on the left-vertically and Labor runs by 2's to 20 horizontally

The first question asks me what price does Impact Imdustries pay for capital. In the text capital and labor units are always given, I can find no formula for determining capital...

Can some one help?!?!?!?!? I'm frustrated!

Thanks,

EY

see my response to your July 15 posting.

## Well, EY, it seems like you're really stuck between a rock and a hard place. Or in this case, between labor and capital units. Don't worry, I've got a joke that might lighten the mood and help you out.

Why don't economists ever become comedians?

Because they can't even make their own graphs funny!

Now, back to your question. Determining the price of capital can be a bit tricky, but luckily, I have a little trick up my sleeve. You can use the information given about the expansion path and the prices of labor to find the price of capital indirectly.

Here's what you can do:

1. Start by calculating the slope of the expansion path between each output level and its corresponding capital and labor units. The slope indicates the ratio of capital to labor units.

2. Since the price of labor is given as $100 per unit, you can use this information along with the capital-labor ratio to find the price of capital at each output level.

For example, at the 120 output level, the expansion path hits the line with 4 labor units and 20 capital units. So, the capital-labor ratio is 20/4 = 5. Since the price of labor is $100 per unit, it means the price of capital is $100 * 5 = $500 per unit.

You can repeat this process for the other output levels (180 and 240) to find the prices of capital at those points as well.

I hope this helps you make some economic sense out of the situation, EY! Let me know if you have any other questions or need more assistance.

## To find the price that Impact Industries pays for capital, you need to use the information provided about the expansion path and the price of labor.

The expansion path shows the levels of capital and labor units at different output levels. For example, at 120 units of output, the expansion path hits 20 capital units and 4 labor units.

To determine the price of capital, you can use the formula for the production function, which relates the output level to the inputs of capital and labor.

In this case, the production function is not explicitly given, but you can approximate it using the expansion path. Since the expansion path is derived from actual production data, it represents the relationship between output, capital, and labor for Impact Industries.

To approximate the production function, you can use a linear interpolation between the available data points. For example, at the output level of 120, the expansion path hits 20 capital units and 4 labor units. At the output level of 240, the expansion path hits 50 capital units and 8 labor units.

Using these two data points, you can find the slope of the expansion path (change in capital units divided by change in labor units). In this case, the slope would be (50 - 20) / (8 - 4) = 30/4 = 7.5.

Since the price of labor is given as $100 per unit, you can use the slope of the expansion path to find the price of capital. The price of labor should be equal to the marginal product of labor (MP_L) multiplied by the price of labor.

MP_L is the additional output produced by an additional unit of labor. In this case, the MP_L can be approximated as the slope of the expansion path.

So, the price of capital would be (slope of expansion path) * (price of labor).

In this case, the price of capital would be 7.5 * $100 = $750.

Therefore, the answer to your question is that Impact Industries pays $750 for capital.

Note: This is an approximation based on the available data points and the assumption that the production function is linear. It is always best to check with the given sources or consult a production economist for accurate information.