show how a total product curve for an input can be derived from an isoquant map.
These sites may help you.
http://en.wikipedia.org/wiki/Isoquant
http://www.lmu.ac.uk/lbs/epia/people/beachill/micro1/mic1top6.doc
This website seems to deal with that question:
http://72.14.253.104/search?q=cache:OX_R_zHSVd0J:www.ssc.wisc.edu/~snavarro/Econ_301/LECTURES/Chapter7.pdf+%22product+curve%22+isoquant+map%22&hl=en&ct=clnk&cd=4&gl=us&ie=UTF-8
It is not a subject I am familiar with, it looks like it would require graphic capabilities that Jiskha does not have.
This pdf version of my previous recommended website has better graphics:
http://www.ssc.wisc.edu/~snavarro/Econ_301/LECTURES/Chapter7.pdf
To derive a total product curve for an input from an isoquant map, you need to follow these steps:
1. Understand the concept of an isoquant: An isoquant shows all the combinations of inputs (usually labor and capital) that can produce the same level of output. It represents the different input combinations that yield equivalent levels of output.
2. Determine the levels of output: Look at the isoquant map and identify the levels of output represented by each isoquant curve. For example, the isoquant curve Q1 represents 10 units of output, the isoquant curve Q2 represents 20 units of output, and so on.
3. Identify the input combinations: Along each isoquant curve, you'll find different input combinations (such as labor and capital) that produce the same level of output. Focus on one specific input, in this case, let's assume we are interested in the total product of labor for a given input of capital.
4. Calculate the total product: For each isoquant curve, calculate the total product by summing up the quantities of output at each input combination. For example, if the isoquant Q1 represents 10 units of output, and the total product of labor at each input combination on this isoquant is 2, 3, 4, and 1, then the total product curve would show a total product of labor as 2, 3, 4, 1 for an input of 10 units of output.
5. Plot the total product curve: Using the input quantities (capital) on the x-axis and the total product of labor on the y-axis, plot the total product curve. Each point on the curve represents the total product of labor for a specific input (capital) level, keeping the output constant as indicated by the corresponding isoquant curve.
By following these steps, you can derive the total product curve for an input from an isoquant map. This curve provides insights into how the input levels affect the overall output and helps determine the optimal combination of inputs to maximize production efficiency.