Question

3. Incentives to make high-end goods/innovations in the market Monty Verdi has invented a better umbrella, for which monthly demand is given by Q = 100 – 2P. (Q is in umbrellas per month and P is in dollars, but you probably already knew that.) 4 (a) (1 point) How much quantity is demanded at P = $15? Į 16 (b) (2 points) If you got (a) correct, you should be able to figure out that the monthly revenue (P*Q) is $1,050. If the per-unit variable costs (which you might think of as “marginal cost") are $5 per unit, how much are monthly profits at a price of $15? (c) (2 points) How many umbrellas must eventually be manufactured and sold at $15, over time, to break even against a fixed cost of $5,000 to design and create the prototype while supporting Monty during the invention process? (d) (1 point) Profit is maximized at a price of $27.50 rather than $15 (you can trust me on this for now, but can check it out later.) How many units must be manufactured at $27.50, over time, to break even against the fixed cost of $5,000 to create the prototype? (e) (1 point) OK, so you've figured out how many umbrellas it takes to break even. How many months does it take to break even at prices of $15 and $27.50, respectively? (You can ignore discounting and the time value of money.) (f) (2 points) After you've broken even, what are the NPVs of the monthly profits at prices of $15 and $27.50 respectively? Use a discount rate of 1% per month. [Think of this as the income that the inventor receives in their old age, once they've retired to the Costa Rican rain forest.] (g) (2 points) Write a few words about the relative importance of the economic sophistication of pricing the umbrella correctly compared to the completely different skill required to invent the umbrella.

Answer 1

Answer:

Given that,

Q=100-2P (Q is in umbrellas per month and P is in dollars

a)

Q=100-2P

at P=15,

Q=100-2(15)

=70

b)

P=50-0.5Q

TR=P*Q

= 15*70

=1050

If MC=AC=5 then TC=5*70

=350

Profit=TR-TC

=1050-350

= 700

c)

At P=15 and Fixed cost is 5000 in order to break even means profits are zero

TR=15*Q and TC=5000+5Q

If profits are zero then TR=TC implies 15Q=5000+5Q

Q=500

d)

If market price changes to P= 27.5 then to break even means

TR=TC

27.5*Q=5000+5Q

22.5Q=5000

Q=222

Note: As per the HOMEWORKLIB RULES, I have solved the first 4 sub-parts of the Question.
Please Re-post for the Rest.

Please comment below if you have any doubts.