# Production Cost Analysis

**Problem 1**

**William Pizza Shop**

Number of ovens= 4

Cost of the ovens= $1,000

Weekly wages of each worker= $500

**Solution/ Workings **

Number of Workers | Quantity of Pizzas Produced (A) | Pizzas Per Worker (B) | Total Weekly Wages (C) | Cost of ovens (D) | Total Cost (D+C) |
Marginal Cost (C/A) |

0 | 0 | 0 | 0 | 1,000 | 1,000 | 0 |

1 | 75 | 75 | 500 | 1,000 | 1,500 | 6.67 |

2 | 180 | 90 | 1000 | 1,000 | 2,000 | 5.56 |

3 | 360 | 120 | 1500 | 1,000 | 2,500 | 4.17 |

4 | 600 | 150 | 2000 | 1,000 | 3,000 | 3.33 |

5 | 900 | 180 | 2500 | 1,000 | 3,500 | 2.78 |

6 | 1140 | 190 | 3000 | 1,000 | 4,000 | 2.63 |

7 | 1260 | 180 | 3500 | 1,000 | 4,500 | 2.78 |

8 | 1360 | 170 | 4000 | 1,000 | 5,000 | 2.94 |

**Which inputs are fixed and which are variable in the production function of William’s pizza shop? **

The fixed costs in the production of pizza include:

- Rent/ Lease
- Operating license
- Cost of each oven

Variable costs

- Labor
- Costs of inputs used in the oven such as flour, electricity, sugar.

**Over what ranges do there appear to be increasing, constant, and/or diminishing returns to the number of workers employed?**

The variable cost of labor has an increasing return to a maximum of 6 workers. Noteworthy, the return for employing a worker is highest when they are 6. An increase of more than six workers (7 or 8 workers) has a diminishing return. In this case, the average return for the workers decreases below the optimal levels attained by six workers.

**What number of workers appears to be most efficient regarding pizza product per worker?**

The most efficient number of workers is 6. Six workers bake 190 pizzas each, which is the highest production level for each worker in the business.

**What number of workers appears to minimize the marginal cost of pizza production assuming that each pizza worker is paid $500 per week?**

Six workers minimize the marginal cost of pizza production. The marginal cost of each pizza, when baked by 6 workers, is 2.63, which is the lowest in the company.

**Why would marginal productivity decline when you hire more workers in the short run after a certain level?**

The reason for the decrease in marginal productivity when you hire more workers in the short run is due to the imbalance in the resources in the firm. For example, the bakery’s ovens have a maximum number of pizzas they can bake; therefore, an increase in the number of workers without a similar increase in the number of ovens will not lead to an increase in production levels.

**How would expanding the business affect the economies of scale? When would you have constant returns to scale or diseconomies of scale? Describe your answer.**

Increasing the size of the business will enable the company to access quantity discounts from its suppliers since it will always make huge purchases. Additionally, the business will be able to use all its resources at their optimal levels, which will result in it having a low production cost. A business always has a constant return to scale when each additional resource can be utilized at its optimal level. For such utilization to happen, the business must have a balance of all its available resources. In William bakery, for example, there must be a direct matching of ovens and laborers. Finally, diseconomies of scale happen when there is a mismatch between the available resources in a company and the added resource. For example, an increase in the number of laborers beyond the current optimal levels not being matched with a similar increase in ovens.

**Problem 2**

**Paradise Shoe Company**

TVC = 3450 + 20Q + 0.008Q^{2}

TVC= Total variable cost

Demand Equation

Q = 4100 – 25P

Current production is 1,000 shoes weekly

Considering to increase to 1,200 pairs of shoes weekly

Business should lease a shoe making machine at $2,000 weekly

**Describe and derive an expression of the marginal cost (MC) curve.**

TVC = 3450 + 20Q + 0.008Q^{2}

Marginal Cost (MC) = 20+ 0.016Q

The marginal cost is derived by differentiating the total variable cost (Braun & Tietz, 2017). Marginal cost shows the cost of manufacturing each additional unit of shoes.

**Describe and estimate the incremental costs of the extra 200 pairs per week (from 1,000 pairs to 1,200 pairs of shoes).**

Estimated cost of the extra 200 pairs= Marginal cost * 200 pairs

MC*200

(20+ 0.015Q)* 200

Total revenue = Quantity * Price

Total revenue (TR)= Q*(4100-Q)/25

TR= (4100Q-Q^{2})/25

MR= (4100-2Q)/25

At profit maximization MR= MC (Datar & Rajan, 2017)

(4100-2Q)/25=20+ 0.016Q

4100-2Q= 500+ 0.4Q

3600=2.4Q

Q= 1500

Incremental cost of extra 200 pairs per week

(20+0.015*1500)200= 8,500

**What are the profit-maximizing price and output levels for Paradise Shoes? Describe and calculate the profit-maximizing price and output.**

At the profit maximizing point, the marginal cost equals marginal revenue (Datar & Rajan, 2017).

Paradise Shoe Company

TVC = 3450 + 20Q + 0.008Q^{2}

MC= 20+ 0.016Q

Demand Equation

Q= Quantity, P= Price

Q = 4100 – 25P

P= (4100-Q)/25

Total revenue = Quantity * Price

Total revenue (TR)= Q*(4100-Q)/25

TR= (4100Q-Q^{2})/25

MR= (4100-2Q)/25

At profit maximization MR= MC

(4100-2Q)/25=20+ 0.016Q

4100-2Q= 500+ 0.4Q

3600=2.4Q

Q= 1500

P= (4100-Q)/25

P= (4100-1500)/25

P= 104

Paradise Shoes Company should manufacture 1500 pairs weekly to make maximum profits from each pair. Any production more or less than 1,500 will result in the company earning fewer profits from each pair. The company should also sell its shoes at $104 per pair. A price of less than $104 will result in the company not making maximum profits, while a price of more than $104 will decrease the demand for the shoes and result in Paradise Shoes making few profits (Datar & Rajan, 2017).

**Discuss whether or not Paradise Shoes should expand its output further beyond 1,200 pairs per week. State all assumptions and qualifications that underlie your recommendation.**

From the analysis, the profit-maximizing output is 1,500 pairs per week. Therefore, Paradise Shoes should increase its output to 1,200. Since the optimal production level is 1,500 pairs, the increase in the number of shoes manufactured from 1,000 to any volume less than or equal to 1,500 will result in Paradise Shoes making more profits.

The assumptions that underlie my recommendations are:

- The marginal costs and marginal revenue will not vary with the increased output.
- The factors of production will retain their current productivity.
- The business will not get any quantity discounts due to the increased production.

References

Braun, K., & Tietz, W. (2017). *Managerial accounting* (5^{th} Ed.). Upper Saddle River, NJ: Pearson.

Datar, S., & Rajan, M. (2017). *Horngren’s cost accounting: A managerial emphasis* (16^{th} Ed.). Upper Saddle River, NJ: Pearson.