Your friend invests and patents a portable ice cream carrier (PCC) which you pla

Question

Your friend invests and patents a portable ice cream carrier (PCC) which you plan to manufacture as well. You determine the demand function for the product is

Q = 120 - 3P while the cost is TC = 2Q

a. what are your profit maximizing price and quantity for this product? what profits will you make?

Suppose your market research leads you to conclude that there are two distinct groups of consumers interested in the PCC, restaurants and homes. You determine that each has a different demand curve as follows

Qrest = 70 - 2P

Qhome = 50 - P



You can easily distinguish between the two by the fact that restaurants have licenses to sell food while homes do not. And because the PCC is adjusted to the average quantity of ice cream being carried by that particular consumer (this is done at the time of the sale) resale is no possible. You decide that this is a great opportunity to engage in 3rd degree price discrimination (charge each group a different price)



b. what price will you charge resaurants and what price will you charge homes? how many PCC's will you sell to each?

Explanation / Answer

1. In this case, if we take the derivative of TC we get MC. We can then set this equal to our demand function which is MR 2=120-3P 3P=118 P=118/3 or 39.33 Q=120-3(118/3)=2 Profits will be 118/3*2=236/3=78.66 2. In this question we will compute similar methods but for both demands Qrest 70-2P=2 68=2P P=34 Q=70-2(34)=2 For our profit 34*2=68 Qhome 50-P=2 P=48 Q=50-48=2 Profit= 2*48=96 Hope this helps

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