Blog Three

Part One:

(Made up company…) Parisian Pastries is where artisan bakers craft the most delicate and tasty pastries that would even make Queen Antoinette say, "Let them eat cake (Parisian Pastries' cakes of course)"! Since their founding, they have been committed to creating pastries that are rich in taste and lavish in style. All their pastries are crafted with one hundred percent organic ingredients and with love. Parisian Pastries brings the "je ne sais quoi" of Paris to you with our signature French macarons and other delectable pastries!  

The company sells French pastries, but the key product examined in the blog assignment will be their signature French macarons. The demographic for the product are humans who love really yummy treats!

Part Two:

Total Fixed Costs:

Rent:  4,000/ month

Utilities (Heat, A/C, Electricity, Water, Gas): 1,000 / month

Internet: 100/ month

Machinery: 400/month

Salary: 10,000/ month

Marketing & Misc: 4,500

= $20,000 / month

Total Variable Costs:

All Natural Powder Sugar: $5

All Natural Almond Powder: $5

Organic Orange Zest: $2

Organic, Free-Range Eggs: $7

Organic Cocoa Powder: $3

Organic Sugar: $8

Total Variable cost/unit: $30 / every additional batch of macarons. Each batch makes around 10 macarons, thus it costs $3 to produce one additional macaron.

Price: The company sells each macaroon for $5 each.

Cost Function:

C(q)= 20,000 + 3q

Revenue Function:

R(q)= 5q

Profit Function:

P(q)= 5q–(20,000+3q)

P(q) = 2q-20,000

Break-Even Point Value:

5q-3q-20,000=0

2q=20,000

q=10,000

10,000 macarons are needed to break even.

Cost and Revenue Function Graph:

Interpretation: The break-even point on the graph is when the company makes $0 and instead breaks even in regards to both fixed and variable. It is the point at which their costs (both fixed and variable) and their revenue are equal. So in regards to the pastry shop, the break-even point will occur when the shop sells 10,000 macarons (units). When the MC > MR, then the company is make a loss, but when the MC < MR, the company is then making a profit as their revenue they are generating is more than the cost of producing.

Profit Function Graph:

Interpretation:

The profit function graph illustrates that the break even point is where the p(q) crosses the x-axis, which in this case is at 10,000 units. When we sell 10,000 units, we can note that we have broken even or made $0 but as we sell more units, we will be then making a profit.

Part Three:

N=12,500 units are produced on a daily basis.

C(12,500) = 20,000+ 3(12,500)

=57,500

Average Cost with q=n

=20,000 +3q / q

=20,000 +3(12,500) / 12,500

=57,500/12,500

=4.6

Marginal Cost and Average Cost Graph:

The marginal revenue is the slop of the c(q) and when finding the slope I calculated (50,000-40,000)/(10,000-5,000) to get y=2. The Average cost is on there which was calculated earlier.

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

The marginal revenue is greater than the marginal cost at q=n (q=12500) because when the company produces 12,500 units the cost is 57,500 (20,000+3(12,500)) and the revenue will be 62,500 because 5x12,500=62,500. With this in mind, we can notice that the revenue is greater than the cost, so they are making a profit.

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

The number sold daily is after break-even point, this means that they are making a profit as they already covered their costs and are now making more money.

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.

Yes, the company will continue to make money. For instance, if we added another unit our formulas will now be:

R(q+1) – R(q) … R(12,500+1) - R(12,500) …

=5(12,500)+1 – 5(12,500)

=62505-62500

=5

C(q+1)-C(q)

C(12,500+1) – C(12,500)

20,000+ 3(12,500) -20,000+ 3(12,501)

=57,500-57503

= -3

As we can see, we will incur an added $3 in costs, but at the same time we will also have a $5 in revenue generated from making the extra unit, thus we can note that 5-3= 2 dollars earned more from the new unit produced.

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

(daily production of 12,500 units average cost)

=20,000 +3q / q

=20,000 +3(12,500) / 12,500

=57500/12500

=4.6

(break-even, 1000 units average cost)

=20,000 +3q / q

=20,000 +3(10,000) / 10,000

=50,000/10,000

=5

When there is an increase in n, the average cost decreases for the company as noted by the fact that when the company produces 10,000 units the average cost is $5, but when the company increases their production to 12,500 then the average cost decreases to $4.6.

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

Decreasing average cost is better for the company because if their costs keep on going down, then they are able to make more money. It is better to have decreasing average costs as that means that the costs are decreasing as you are producing more, thus in general it is costing your company less to produce more units.

6) Provide an analysis of how you think the company will do over the next five years based on all of the information you have gathered from your experiment. 

The company will probably thrive in the next five years because for starters everyone loves to eat yummy treats and macarons are all the demand right now. Yes, the demand may decrease later on as people may move towards eating cupcakes, cakes, or some other pastry, but to be honest, macarons are a classic delicious treat and they will never go out of style once people taste their first bite! Additionally, the company will do well as they are making a profit on a daily basis and if they continue at the rate they are now of making a profit of $5,000 a day [(2x12500)-20000] and $5,000 a day profit x 365 days for one year is $1,825,000 for their annual profit. If they continue to make and sell 12,500 units then I would say they are going to be fine.