Question

Panama Jack has invented a better infrared toaster oven, for which monthly demand is given by Q = 400 – 4P. (Q is in ovens per month and P is in dollars.)

a. (1/2 point) How much quantity is demanded at P = $50?

b. (1 point) If you got (a) correct, you should be able to figure out that the monthly revenue (P*Q) is $10,000. If the per-unit variable costs (which you might think of as “marginal cost”) are $35 per unit, how much are monthly profits at a price of $50?

c. (1 point) How many ovens must eventually be manufactured and sold at $50, over time, to break even against a fixed cost of $60,000 to design and create the prototype while supporting Jack during the invention and innovation process?

d. (2 points) It turns out that a price of $50 (and the quantity you found in (a)) maximizes revenue, but does not maximize profit. Equate marginal cost with marginal revenue to find the profit-maximizing price and quantity. If you can’t do this, simply plug in a quantity of 160 and go on.

e. (1 point) How many units must be manufactured at P* [the profit-maximizing price found in (d)], over time, to break even against the fixed cost of $60,000 to create the prototype?

f. (2 points) OK, so you’ve figured out how many ovens it takes to break even. How many months of production does it take to break even at prices of $50 and the profit-maximizing price found in (d), respectively? (You can ignore discounting and the time value of money, but don’t forget the Law of Demand!)

g. (1 points) As the inventor, Jack was planning to charge $50 for the oven. A strategic investor offers to rent Jack a manufacturing facility that will reduce Jack’s marginal cost from $35 to $25. If price stays at $50, what is Jack’s maximum willingness to pay (per month) for such a deal?

h. (2 points) After consulting with a pricing expert, Jack was planning to charge P*, the profit-maximizing price in [d]. At that price, what is Jack’s maximum willingness to pay (per month) for such a deal now?

i. (2 points) Comment on the cause(s) of the difference between your answers to (g) and (h). (Extra credit, 1 point) If Jack accepts the deal, is the price in [d] still the right price to charge? Why or why not?

Please answer question e.f.g.h.i

Answer 1