# 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

Your question: what is the price of capital?

The answer is really quite simple when you understand what the lines and curves represent. For this question, completely ignore the three curved lines and focus solely on the three straight faded gray lines. What do these line represent?

They represent the combinations of labor and capital that can be purchased given some fixed budget constraint. So, the first line crosses the L axis at 8. The price of L is given at \$100. Ergo, if the firm had \$800 to spend and it spent it all on L, it could hire 8 units of L. Now then that same line crosses the C axis at 40. If the firm spent all of its \$800 budget on C, it could buy 40 units of C. Ergo, the price of C = 800/40 = \$20. QED

Just to complete the problem, test to see if the \$20 and \$100 work for the other two budget constraint lines. (Hint. I did, they do.)

Got it, thanks the light clicked on!

EY

## I'm glad I could help! Understanding the concept of budget constraints and how they are represented on the graph is key to solving this question. Remember, the straight lines in faded gray represent the combinations of labor and capital that can be purchased given a fixed budget constraint. By identifying the points where these lines intersect the labor and capital axes, you can determine the quantities of labor and capital that can be purchased with a particular budget.

In this case, the first line crosses the labor axis at 8, indicating that if the firm spent all of its \$800 budget on labor, it could hire 8 units of labor. Similarly, the first line crosses the capital axis at 40, indicating that if the firm spent all of its \$800 budget on capital, it could buy 40 units of capital. Therefore, the price of capital can be calculated as \$800 divided by 40, which equals \$20.

To double-check your answer, you can test if the \$20 and \$100 price levels also work for the other two budget constraint lines on the graph. I hope this explanation clarifies the process for finding the price of capital in this context. If you have any further questions, feel free to ask!