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# Plotting Charts and Other Computations using Excel

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1.a) Construct a column chart to visually represent these data (see attachment 1).
1.b) Construct a stacked bar chart to display the sub-categories where relevant. (Note that you will have to compute additional subcategories, for instance, under Family households, this will have to be done for the number of families without children under 18, so that the total of the subcategories equals the major category total. The sum of all categories does not equal the total.)
1.c) Construct a pie chart showing the proportion of households in each category.

2) Compute the relative frequency and cumulative relative frequency of the age groups (see attachment 2). Also, estimate the average age of the sample of respondents. What assumptions do you have to make to do this?

#### Solution Preview

Creating the column chart:
1. Column chart can be made by highlighting the entire data set.
2. Go to Insert --> Column.
3. Then select the column chart that you want.
Note: See the attached file entitled "Guide to Attachment 1. xlsx" for reference.

Creating the stacked bar chart:
Note: It would be impossible to plot an accurate stacked bar when subcategories do not add up to the total.
- In this case, only general categories of ...

#### Solution Summary

The solution shows how to plot stacked bar chart, pie chart. It also shows how relative frequency, cumulative frequency, and average age are computed using Excel. Excel files are attached as guides.

\$2.19

## Graphing Marginal Product and Average Product for three different types of production functions (linear, quadratic, cubic)

Given algebraic equations, need to graph the marginal product and average product for linear short-run, quadratic short-run, and cubic short-run production functions. Plug in numbers to graph. See attachment.Thank you.

Production Functions (Algebraic)

Graph the marginal product (MP) and average product (AP) for each of the following equations by plugging in numbers. (Graph the highlighted equations).

1. Linear Short-run. N = labor
a. MP n = the change in output / the change in labor
= dQ / dN = b

b. AP n = Q / N = a/N + bN/N
= a/N + b

Example: Supppose b = 10 10 + 5/1 = 15
a= 5 10 + 5/2 = 12 ½
N = 1 10 + 5/3 = 11 2/3

Make Y-axis Q (output) and X-axis N (labor) and graph.

Q = a + bN - cN²

a. MPn = dQ/dN = b - 2cN

b. APn = Q/N = a/N + bN/N - CN² / N

= a/N + b - CN

3. Cubic Short-run
Q = a + bN + cN² - dN³

a. MPn = dQ/dN = b + 2c&#8319; - 3dN²

b. APn = Q/N = a/N + bN/N + CN²/N - dN³/N

= a/N + b + CN - dN²

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