Question

Marginal Productivity of Labor

There is enough demand for donuts at Henions that the owner thinks she might be able to justify installing another fryer. Estimates of output for different numbers of workers with one fryer or with two are shown in the table below. After taking account of the cost of ingredients, Henions sells its donuts for $2.50.

Graph the value of total output with one and with two fryers.

What happens to output as more workers are hired with one and with two fryers? What happens to the rate of change in output Why?

Why does output rise with an additional fryer?

Use the data in the graph to answer the following:

How many workers will be hired and how many doughnuts made with one fryer and a wage of $45? With a wage of $25? How many workers will be hired and how many cookies made with two fryers and a wage of $45? With a wage of $25? Why are more hired with two fryers?

Since output is greater with two fryers, would you necessarily recommend that Henion’s buy a second fryer? Give two considerations you might consider in addition to the productivity effect.

Workers	Donuts: one fryer				Donuts: two fryers
	Total output	Value of output	MP	MRP	Total output	Value of output	MP	MRP
1	30				30
2	56				60
3	78				88
4	96				114
5	110				138
6	120				160
7	126				178
8	128				192
9	126				202
10	120				208

Answer 1

A).

Consider the given problem here the price of donuts is “$2.5”, => the value of donuts is given by “P*Q”, => given the information in the table we can get the “value of donuts” with “1 fryer” and “2 fryer”.

Consider the following table shows the “Total Value of donuts”.

Now, in the above table we can see that as “L” increases the production of “donuts” also increases with “1 Fryer” but after “8 workers” it starts decreasing, => “total production=TP” is increasing initially then starts falling. Now with 2 fryer TP is increasing, => as “L” increases implied “TP” increases, => the TP for 2 fryer is upward sloping.

B).

Now, the rate of change measure the MP, => additional production by hiring additional “L”, => the MP for the two possible case are given in the above table. So, here we can see that the MP is falling in both the cases, => as more “L” are hired the “TP” will decrease regard less of number of fryer. This is because of the “diminishing marginal productivity”, => given the number of fryer as we hire more and more “L” leads to inefficiency in the production process, => the additional production decreases, => MP is decreasing.

C).

Now, given the data as number of fryer increases the TP also increases given “L”, => output increases as number of fryer increases.Since, the “L” are best utilized as we have more fryer, => output increases as number of fryer increases.

D).

Now, at the optimum “W=MRP”, => additional cost of hiring “L” must be equal to the additional revenue generating from it. So, with “1 fryer” the optimum “L” is “4”, => for “L=4” “MRP=W=45” and with “2 fryer” the optimum “L” is “7”, => for “L=7” “MRP=W=45”. Now, if “W=25”, => the optimum “L” is “6” with 1 fryer and for 2 fryer the optimum “L” is “9”.

So, if “W=45”, => the production is “96” with 1 fryer and “178” with 2 fryer. Similarly, if “W=25”, => the production is “120” with 1 fryer and “202” with 2 fryer, => if we have more fryer we should hire more “L”, because the “L” are best utilized as we have more fryer, => we have more output.

E).

Here “P” is given and number of fryer increases implied optimum “L” also increases, => it is profitable to have two fryer compare to 1, => we should recommend Henion to buy 2 fryer.