production problem

Bahlman_Chapter_4_Production_Problem_Start.xlsx

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Problem

Production Problem
Cakes by Monica (a bakery under the umbrella of the Café Brulé restaurant) in Vermillion, SD makes cupcakes for customers to purchase both in the store and in bulk orders for birthday parties and weddings. Suppose in the short-run, a bakery like Cakes by Monica has a fixed amount of capital but can hire college students from a local college easily to increase production as needed. A production schedule is provided for you where Q is dozens of cupcakes.
a)	Using the schedule provided, calculate the marginal and average products of labor when K = 3.
	K = 3	L	Output (Q)	MPL K = 3	APL K = 3
	3	0	0
	3	1	10
	3	2	25
	3	3	45
	3	4	60
	3	5	70
	3	6	75
	3	7	75
	3	8	70
	3	9	60
b)	Using your calculations, for which workers are there increasing, decreasing, and negative marginal returns to labor?
		Low	High
	Increasing
	Decreasing
	Negative
с)	Suppose this bakery decides to add another unit of capital in the long-run. Using the schedule provided, find the marginal product of the 4th unit of capital and the marginal and average products of labor when K = 4.
	K = 4	L	Output (Q)	MPL K = 4	MPK	APL K = 4
	4	0	0
	4	1	15
	4	2	35
	4	3	60
	4	4	80
	4	5	95
	4	6	105
	4	7	110
	4	8	110
	4	9	105
d)	Create a graph of the marginal and average products of labor for K=3 and K=4.
e)	Using your graph and the data, does the addition of another unit of capital increase, decrease, or not change the productivity of labor?
			The addition of another unit of capital		the productivity of labor.

Instructions

Project Description: In this problem, you will calculate the marginal and average products of labor, the marginal product of capital and determine the effect of the additional unit of capital on the productivity of labor. You will also create a line chart for the marginal and average products of labor.
For the purpose of grading the project you are required to perform the following tasks:
Step	Instructions	Points Possible
1	Start Excel.	0
2	In cells F8-G8, do the following: In cell F8, by using relative cell references, calculate the marginal product of labor when K = 3. Use cells E7 and E8. Copy the formula from cell F8 down the column to cell F16. In cell G8, by using relative cell references, calculate the average product of labor when K = 3. Use cells E8 and D8. Copy the formula from cell G8 down the column to cell G16.	4
3	In cells D19-E21, do the following: In cells D19-D21, by using cell references, enter the lowest number of workers for which marginal returns to labor are increasing, decreasing, and negative, respectively. Use appropriate cells among D8-D16. In cells E19-E21, by using cell references, enter the highest number of workers for which marginal returns to labor are increasing, decreasing, and negative, respectively. Use appropriate cells among D8-D16.	2
4	In cell F25, by using cell references, calculate the marginal product of labor when K = 4. Use cells E24 and E25. Copy the formula from cell F25 down the column to cell F33.	2
5	In cell G25, by using cell references, calculate the marginal product of the 4th unit of capital. Use cells E8 and E25. Copy the formula from cell G25 down the column to cell G33.	2
6	In cell H25, by using cell references, calculate the average product of labor when K = 4. Use cells D25 and E25. Copy the formula from cell H25 down the column to cell H33.	2
7	In cells C35-G47, insert a Line Chart for the marginal and average products of labor for K=3 and K=4. Inserting Chart Select the Line chart from the provided chart options in the Charts group of the Insert tab of the Ribbon. Selecting Data Series Then choose Select Data in the Design tab on the Ribbon. Delete any series created automatically using the Remove button and add new series for the marginal product of labor for K=3 using the Add button. Select the range of data using cells F8-F16. Use cell F6 as the series name. Add new series for the average product of labor for K=3. Select the range of data using cells G8-G16. Use cell G6 as the series name. Add new series for the marginal product of labor for K=4. Select the range of data using cells F25-F33. Use cell F23 as the series name. Add new series for the average product of labor for K=4. Select the range of data using cells H25-H33. Use cell H23 as the series name. Edit Chart Elements On the Ribbon, select design Style 1. Delete the chart title. Go to the Add Chart Elements dropdown list in the Design tab of the Ribbon. Add the legend and choose the Bottom option. Chart Size and Position Go to the Format tab on the Ribbon. Set the chart height to 3.5 inches and the chart width to 6 inches. Drag the chart to position the entire chart so that it fits within cells C35-G47.	4
8	In cell F49, determine whether the addition of another unit of capital increases, decreases, or does not change the productivity of labor.	1
9	Save the workbook. Close the workbook and then exit Excel. Submit the workbook as directed.	0