There are 2 potential customers, each of whom is interested in buying 1 unit of Link (either Link Professional or Home but not both). Suppose that your objective is to maximize the total revenue from selling the software. Further, you do not know the identity of either buyer and you must sell by posting one price for Link Professional and another price for Link Home. Each buyer seeks to maximize her consumer surplus and may buy Link Professional or Link Home or neither depending on the prices that you post. Please show all intermediate steps and clearly explain your reasoning. i. What is the optimal price and resulting revenue under the following scenario? What (if anything) would each customer buy?
ii. If you could identify each buyer and make targeted offers, what price would you offer to each and how much revenue would you earn? What (if anything) would each customer buy'?
Scenario The willingness to pay (WTP) of the 2 potential buyers is:
Link Professional Link Home
WTP of Buyer A 600 400
WTP of Buyer B 500 300

Step-by-step explanation:

(A)

(i) The optimal price you should post for each of LP and LH is in two combinations:

COMBINATION 1:

$600 for LP and $300 for LH

This combination fetches you $900 (which is the maximum you can earn in this scenario, because each buyer will only buy 1 type of link)

COMBINATION 2:

$500 for LP and $400 for LH

This combination also fetches you $900 revenue.

Why these price combinations? Because you have two constraints:

1. Each buyer is only interested in 1 unit of 1 link type

2. You as a producer or seller, wish to maximize revenue

These are the constraint functions!

(ii) At Price Combination 1,

Mr. A will purchase 1 unit of LP while Mr. B will purchase 1 unit of LH

At Price Combination 2,

Mr. A will purchase 1 unit of LH while Mr. B will purchase 1 unit of LP

(B)

(i) If you could identify each buyer and make targeted offers (offers targeted at each buyer's WTP) you would offer their maximum WTP price to them for each commodity.

That's the 'economic agent' way of thinking; to bargain favourably or in your own case, to maximize revenue.

So, you'll charge Mr. A $600 for LP and $400 for LH

Charge Mr. B $500 for LP and $300 for LH

(ii) Although you thought economically, this particular set of potential customers are price-driven instead of taste-driven so instead of them to purchase LP which is generally more expensive (or of a higher quality), each of them would buy LH!

Your revenue here will now be $400 + $300 = $700

step-by-step explanation:

let's first notice, the center of the hyperbola is at the origin, since the focus points are equidistantly 3 units away from the origin, that also means that the distance "c" from the center to either focus is 3.

it should also be notable that, the traverse axis for this hyperbola is vertical, or namely over the y-axis and therefore, the positive fraction will be the one with y-variable.

the traverse "a" component or distance from the center to either vertex is not 2, is more than 2, so we can safely put it at √5 ≈ 2.24.