Marginal analysis- Ana Maria Lopez

Marginal analysis

Blog submission number 3

Due Date: March 30, 2015 by 11:59 pm

Ana Maria Lopez

Part 1:

This is a company I created, DC shirts, makes personalized t-shirts. The initial cost to start up the company or the fixed cost was $50,000. The cost of producing one t-shirt is $15. The company sells the t-shirts to the general public for $25.

Part 2

·      Fixed cost: $50,0003

·      Variables costs: $15

·      Price for which the company sells a unit/quantity of good: $25

·      Cost function: C (q)= 50,000 + 15(q)

·      Revenue function: R (q)= 25q

·      Profit function: P (q)= 25q - 50,000 +15 (q)

·      Break-even point: C (q)= R (q)

 25q = 50,000 + 15(q)

 10q = 50,000

 q= 5,000

·      Graph for the Cost and Revenue function

The breakeven point is the grey point at (5000, 125000)

·      The marginal cost for making an extra t-shirt is the slope and the derivative of the cost function, which is equal to: $15

·      The marginal revenue of making an extra t-shirt is the slope of the revenue function, which is: $25

·      The break-even point is the point where both functions (cost and revenue) meet. This point is where both of these functions are equaled and it means that in order for the company to make a profit, DC Shirts must make 5,000 t-shirts. When producing 5,000 t-shirts, they would make revenue of $125,000 and spend in costs a total of $125,000 too. This means that to make a profit they must make 5,000 t-shirts or more. When more than 5,000 t-shirts are produced, the marginal revenue surpasses the marginal cost. Since the marginal revenue function continues to get steeper, it gets steeper than the marginal cost line. This signifies that after the break-even point on the graph, the revenue is increasing more than the cost.

·      Graph for the profit function

The breakeven point for this graph is at (5000,0)

·      The break-even point in this graph is when 5,000 t-shirts are being produced, which means that the profit is 0. This means that any amount of t-shirts below 5,000 will result in a loss of money and any amount above 5,000 t-shirts will result in a profit. This is clearly shown in the graph since any amount of t-shirts below 5,000 is negative on the graph and any amount of t-shirts above 5,000 is positive in the graph. Additionally, the slope for the profit function is positive.

Part 3:

·      The number of t-shirts DC t-shirts should produce per day is 500, so q=500 on a daily basis.

·      The marginal cost for producing the nth unit is $15, which can be determined by taking the derivative of the cost function.

·      The average cost of producing the nth unit is Cost function/total quantity which is: 57,500/500=115

·      Graph of the slopes of the marginal cost of q = n and the average cost of q = n.

1.     Is the marginal revenue less than or greater than the marginal cost at q = n? Explain.

·      At q= 500, the marginal revenue is greater than marginal cost because when the quantity of shirts is equal to 500, the marginal cost is $15 and the marginal revenue is $12,500. This means that the revenue is exceeding the cost, which means that the company is making profit.

2.     Is the number of units sold daily (q =n) after or before the break-even point? What does this mean?

·      The number of units sold daily or 500 t-shirts, is before the break-even point of 5,000. This means that DC t-shirts will start off the business operations with no profit or loss but eventually will make profit when they reach the breakeven point.

3.     If production is increased by one extra quantity per day (i.e. if q = n + 1)) will the company continue to make money? Explain. (be sure to reference the formulas R(q + 1) – R(q) and C(q + 1) – C(q) in your explanation)

·      In this case there will still be profit because each extra quantity produced, the marginal revenue is of $12,500 and the marginal cost is only $15. So R(500+1)-R(500) is 12525-12,500= $25. In this case the revenue would be $25.  Also, C (501)-C (500) is 57,515-57,500= $15. In this case the marginal cost of producing one more is $15 and the marginal revenue of producing one more is  $25, meaning there is a profit of $10.

4.     At q = n, does an increase of production increase or decrease the average cost for the company?

·      In this case, an increase in the t-shirt production will mean a decrease in the average cost because for this example the average cost is greater than the marginal cost.

5.     Explain whether increasing or decreasing average costs would be better for the company.

·      A decrease in the average cost is a good sign for DC T-shirts since it means that there are maximizing the company’s total profit. It also means that the cost of production is in general decreasing meaning they can get even more profit from selling the product at the same price of $25, this means that they are inversely related.

Part four

·       I believe that over the next five years, my company will thrive because it has a positive profit function, along will a very low cost of production compared to the possible selling price of $25. Even though I am aware that since DC is a big and developed city and there is a lot of competition, DC t-shirts still has a good chance. Since DC is known for being a really socially and politically active city and many protests and marches are done in this area, there is a high demand for personalized t-shirts for all of these causes. For example, if there is a huge march on pro-choice, many groups of people or a big organization will be looking forward to make personalized t-shirt for the event and cause. I believe there is a high demand for personalized t-shirt in DC. Even though it will take at least 5,000 t-shirts to be sold to make up for the fixed costs plus the additional cost of production of each t-shirt, which means that the company will start operations will losses, I believe it is not that hard to reach this goal and even surpass this amount in order to make profit.