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I'm trying to solve a question that is quite difficult for me. I did part of the question but, bit difficult to decide the exact answer for the below question.

After coming up with an innovative idea for a new product, you paid 4000 to an industrial designer to draw the blueprints and found a factory in China that agreed to produce the product for you for $3 per unit (the price includes the shipping cost from China to you).

Since this is a totally new and unique product, you have no idea how the demand for it would be. Therefore, before you start pricing the product and ordering large amounts from the Chinese factory, you decide to run an experiment (or a pilot study): you talk to Target and they allow you to sell your product at 11 different Target stores for 11 different prices (a different price at each store). These stores are located in areas whose residents have similar average income, so you can be certain that price (and not income) is the only factor varying among these stores.

After 2 weeks, Target sends you the sale numbers for your product.

Price   Quantity Demanded
4   221
5   210
6   185
7   162
8   144
9   122
10  102
11  81
12  61
13  46
14  25

What they are asking is to measure the total fixed cost and the marginal cost.

Can 4000 be decided as the fixed cost? If so how the marginal cost can be calculated? I believe the variable cost is 3$. This 4000 should be only the initial fixed cost. How can I calculate the marginal cost.

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The marginal cost is 3. Marginal costs do not depend on the fixed cost, and when your variable costs are constant, then the marginal cost and the variable cost are the same. Note that your total cost is $C=FC+3q$ and the marginal cost is always the derivative of your total cost, in this case, $3$.

As for the fixed costs, 4000 is definitely part of it, but maybe also the forgone profits from selling the goods in the various stores at sub-optimal prices, as pointed out by another response. Other's have pointed out that if you calculate the variable profits for each price, 9 gives the largest profits, so in all the other stores that you made less profits, the lost profits should probably be added to the fixed cost.

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  • $\begingroup$ Thanks Gabrial, do you have any tutorials that I can refer for further information. $\endgroup$ – Hiru Apr 22 at 6:56
  • $\begingroup$ I did a small change difference to my question, Can you kindly check whether it is correct as well $\endgroup$ – Hiru Apr 22 at 7:03
  • $\begingroup$ Hi, unfortunately I do not know of any tutorials online. Also I cannot find what changed in the question. Do you mind pointing it out? The more I see the question, the more I'm convinced that the fixed costs should be the sum of what you paid to the designer (4000) plus the cost of the experiment. For example, compute all the variable profits for each price using the formula $\pi=(p-mc)q$, so that, for example for a price of $4$, you get: $(4-3)*(221)=221$ However, after running the experiment you realized that the optimal price is $9$ (compute all variable profits to realize this is the case) $\endgroup$ – Regio Apr 22 at 17:03
  • $\begingroup$ So the optimal profit is $(9-3)*122=732$ this means that in the first store where you sell it at a price of $4$ you could have made $732$ but did $221$. The difference $732-221=511$ are part of the fixed cost, as is the implied cost of the experiment. So you want to calculate these costs for every store you experimented in. $\endgroup$ – Regio Apr 22 at 17:08
  • $\begingroup$ Thanks alot for the explanation Gabriel $\endgroup$ – Hiru Apr 23 at 1:27

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