Question

_{Production and Costs Homework #5 Please answer all questions and each part}

_{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

Quantity of Labor	Quantity of cupcakes (TPP)	MPP	TVC	TFC	TC	MC	AVC	AFC	ATC
		Tppn-TPPn-1			TVC+TFC	TCn-TCn-1	TVC/output	TFC/output	TC/output
0	0	-	0	100	100	-	0
1	110	110	80	100	180	80	0.73	0.91	1.64
2	200	90	160	100	260	80	0.80	0.50	1.30
3	270	70	240	100	340	80	0.89	0.37	1.26
4	300	30	320	100	420	80	1.07	0.33	1.40
5	320	20	400	100	500	80	1.25	0.31	1.56
6	330	10	480	100	580	80	1.45	0.30	1.76

MPP	Marginal Physical Product
TVC	Total Variable Cost
TFC	Total Fixed Cost
TC	Total Cost
MC	Marginal Cost
AVC	Average Variable cost
AFC	Average Fixed Cost
ATC	Average Total Cost

1. Her variable inputs - workers, flour , frosting.  Fixed inputs - mixers ( 3 of them)

2. The marginal product of 1st worker - 110 , 2nd worker - 90 , 3rd worker - 70

The marginal product decreases due to application of "law of diminishing marginal productivity/returns". This law states that as the output increases with an additional unit of labor, the increase in output keeps on falling.

This can be attributed to the fact that the , with fixed inputs and only variation in the workers, only till a certain point the extra workers can bring in extra output. At the beginning, the fixed input ( mixer ) is being under-utilized so, as the workers increase the fixed input is being used more efficiently . Once, the fixed input is fully utilized then, beyond that point the extra workers will not bring in extra output.

So, the substitution of labor for the fixed input can happen only till one point.

3. The total variable cost is $80 multiplies by the no. of workers. So, at 110 it is $80 , 200- 160.

4. Marginal cost for 110 cupcakes is - $80 , for next 90 cupcakes - $80.

5. Since, the fixed cost is the same throughout which is $100. As, the output increases the fixed cost is spread across a higher output and hence, keeps falling but will never go below 0.

6. The fall in AVC is due to the operation of diminishing returns which causes the cost to rise.

7. 270 cupcakes will be produced when ATC is minimized. (ATC=1.26)