Question

Servings	MU boeuf bourguignon
1	$60.00
2	$58.00
3	$56.00
4	$54.00
5	$52.00
6	$50.00
7	$48.00
8	$46.00
9	$44.00
10	$42.00
11	$40.00
12	$38.00
13	$36.00
14	$34.00

Production. Ella makes boeuf bourguignon using equipment that she rents for $75 and beef, potatoes, wine and other ingredients that cost $12.50 a serving. (Note that she signed a lease and pays the rent regardless of how many dinners she serves.) She hires workers at $25 each and finds that they produce servings according to the following schedule:

Servings	Total Workers
1	0.30
2	1.00
3	1.90
4	3.00
5	4.30
6	5.80
7	7.50
8	9.40
9	11.50
10	13.80
11	16.30
12	19.00
13	21.90
14	25.00

a. Calculate and graph the marginal cost of each serving. (Use a spreadsheet show all your calculations!) Why does the MC curve have the slope (up, down, or flat) that it does?

b. Calculate and graph the marginal cost of each serving if workers become more productive so each serving can be made with only 70% as much labor. Show your calculations! Calculate and graph marginal cost if workers suffer a 30% pay cut with the old productivity. Compare the effect on MC of the productivity increase with the pay cut.

Answer 1

Consider the given problem here “Serving = Y” and the “worker = L” is given in the question. Consider the following table showing the “MPL”, MC of making “boeuf bourguignon”.

Where “MPL” is “?Y/?L” and “MC=W/MPL”. So, here the MPL is decreasing and the wage rate “W” is constant, => “MC” the ratio of “W” and “MPL”, => “MC” is upward sloping.

b).

Now, as the marginal productivity increases, => to produce the same amount of “Y”, the labor requirement decrease by “30%”, => the same “Y” can be produced by using “70%” of the initial labor requirement. Consider the following table shows the combination of “Y” and “L” under the given situation and the corresponding MC.

Here the new labor “L’” is “70%” of the old labor “L” and "MC_2" be the MC under this situation.

Now, suppose “L” remain same but “W” decrease by “30%”, => the wage will be “0.7*25”. So, under this situation the “MC” is given below in the following table.

So, if we compare these cases then we will find that in both the cases the “MC” is same , => “30%” decrease in “W” and “30%” decrease in labor requirement is same, since in both the cases we will get same MC, => both have same effect on MC.