Question

Marty’s Frozen Yogurt is a small shop that sells cups of frozen yogurt in a university town. Marty owns three frozen-yogurt machines. His other inputs are refrigerators, frozen-yogurt mix, cups, sprinkle toppings, and, of course, workers. He estimates that his daily production function when he varies the number of workers employed (and at the same time, of course, yogurt mix, cups, and so on) is as shown in the accompanying table.

Quantity of labor ( Workers )	Quantity of Yougart (Cups)
0	0
1	110
2	200
3	270
4	300
5	320
6	330

a. What are the fixed inputs and variable inputs in the production of cups of frozen yogurt?

b. Draw the total product curve. Put the quantity of labor on the horizontal axis and the quantity of frozen yogurt on the vertical axis.

c. What is the marginal product of the first worker? The second worker? The third worker? What pattern does the marginal product exhibit for this data?

d. Find the average product for each amount of labor. Do you think, is there any amount of labor where both marginal and average product are equal? If yes than where, and if not than why?                                                                                                                                                             

Answer 1

a) * Fixed input.

1)Frozen yogurt machine

2)Refrigerators

These are inputs which doesn't vary with the quantity of output produced.

* Variable input

1) frozen yogurt mix

2) cups

3) sprinkle toppings

4) workers

These are inputs that doesn't vary with output.

b)

c) marginal product of Labour is the addition to total product when one more unit of labour is used in the production.

MPL = ∆ TP/ ∆ L

∆ TP = change in total product

∆ L = change in Labour input.

* Marginal product of the first worker = (110-0)/1 =110

* Marginal product of the second worker = ( 200-110)/1 =90

* Marginal product of the third worker = ( 270-200)/1 =70

* Marginal product is exhibiting a declining trend.

d) Average product can be obtained using the following formula.

APL = TP/ L

TP = total product

L = quantity of labour input used

Average product.

_

110/1 =110

200/2 = 100

270/3 = 90

300/4 = 75

320/5 = 64

330/ 6 = 55

when only one unit of Labour is used average product is equal to marginal product. This happens because, marginal product curve intersects average product curve when average product is maximum.ln our example, average product is maximum when one unit of Labour is used in production.