Question

_{Production and Costs Homework #5}

_{The following information that apply to Lisa’s Cupcake Shoppe should be used to answer the questions.}

Quantity of Labor (workers)	Quantity of cupcakes (TPP)	MPP	TVC	TFC	TC	MC	AVC	AFC	ATC
0	0
1	110
2	200
3	270
4	300
5	320
6	330

1. _{Lisa’s Cupcake Shoppe is a small shop that sells cupcakes in a university town. Lisa owns three mixers.  Her other inputs are ovens, flour, cupcake tins, frosting and of course, workers.  She estimates that her daily production function when she varies the number of workers employed (and at the same time, of course, flour, frosting, etc.) is as shown in the accompanying table.}

1. _{What are the fixed inputs and variable inputs in the production of cupcakes?}
2. _{What is the marginal product of the first worker? The second worker? The third worker?}
3. _{Why does marginal product decline as the number of workers increases?}

2. _{The production for Lisa’s Cupcake Shoppe is given in Problem 1.  Lisa pays each of her workers $80 per day, including the costs of her other variable inputs.  Her fixed cost is $100 per day.}
   1. _{What is Lisa’s variable cost and total cost when she produces 110 cupcakes? 200 cupcakes? Calculate the total variable cost (TVC) and total cost (TC) for every level of output given in Problem 1.}
   2. _{What is the marginal cost per cupcake for the first 110 cupcakes? For the next 90 cupcakes? Calculate the marginal cost (MC) for all remaining levels of output.}
   3. _{For each level of output, calculate the average fixed cost (AFC), average variable cost (AVC), and average total cost (ATC) per cupcake.}

3.        _{a. What principle explains why the AFC declines as output increases? Explain your answer.}

_{b. What principle explains why the AVC increases as output increases? Explain your answer.}

_{c. How many cupcakes will be produced when ATC is minimized?}

Answer 1

We have the following information

Quantity of Labor (Workers)	Quantity of Cupcakes (TPP)	MPP	Wage Rate ($)	TVC ($)	TFC ($)	TC ($)	MC ($)	AVC	AFC	ATC
0	0	--	80	0	100	100	--	--	--	--
1	110	110	80	80	100	180	80	80	100.0	180.0
2	200	90	80	160	100	260	80	80	50.0	130.0
3	270	70	80	240	100	340	80	80	33.3	113.3
4	300	30	80	320	100	420	80	80	25.0	105.0
5	320	20	80	400	100	500	80	80	20.0	100.0
6	330	10	80	480	100	580	80	80	16.7	96.7

For Lisa, three mixers and ovens are the fixed cost. The variable cost faced by Lisa includes flour, cupcake tins, frosting and workers.

Marginal product of labor (MPP) is the additional output produced as the labor input is increased by 1 unit.

As one can see from the table, the MPP declines as the number of workers is increased. This happens because as the use of an input increases in equal increments with other inputs fixed, a point will eventually be reached at which the resulting additions to output decrease. When the labor input is small as compared to the fixed input, extra labor adds considerably to output, often because of increased specialization. However, as the number of workers increases, there comes a time when there are too many workers, as a result of which some workers become ineffective and the marginal product of labor falls.

When ATC is minimized ($96.7), then the total amount of output produces is 330.