Question

Panama Jack has invented a better infrared toaster oven, for which monthly demand is given by Q 400-8P. ( ovens per month and P is in dollars.) l- 200 a) (1/2 point) How much quantity is demanded at P- $25 b) (1 point) If you got (a) correct, you should be able to figure out that the monthly revenue (P*Q) is $5,000. If the per-unit variable costs (which you might think of as "marginal cost") are $15 per unit, how much are monthly price of $25? 0003ooo ee o00 5000 1 point) How many ovens must eventually be manufactured and sold at $25, over time, to break even againsta fixed co (c) ( st of $70,000 to design and create the prototype while supporting Jack during the invention and innovation process? (d) (2 points) Iit turns out that a price of $25 (and the quantity you found in (a)) maximizes revenue maximize profit. profit-maximizing price and quantity. If Make your EC 301 professor proud: equate marginal cost with marginal revenue to find the you can't do this, simply plug in a quantity of 160 and go on. t) How many units must be manufactured at Pe [the profit-maximizing price found in (e)], over time, to break even against the fixed cost of $70,000 to create the prototype? (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 $25 and the profit-maximizing price, respectively? (You can ignore discounting and the time value of money, but don't forget the Law of Demand) (f) (8) (1 poi ints) As the inventor, Jack was planning to charge $25 for the oven. A strategic investor offers to rent Jack facility that will reduce Jack's marginal cost from $15 to $10. If price stays at $25, what is Jack's a manufacturing 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 . At that price, what is Jack's maximum willingness to pay (per month) for such a deal now? (0) (2 points) Comment on the cause(s) of the difference between your answers to (g) and (h) 0) (Extra credit, 1 point) If Jack accepts the deal, is the price in le) still the right price to charge? Why or why not?

Answer 1

Q = (400 - 8P) or Q = {400 - 8 (25)} = 200 units (b) VC = MC = AC = $ 15 per unit Since VC = AC, The total cost of producing 200 units = (200 times 15) = $ 3000 So profit = (TR - TC) = 5000 - 3000 = $ 25000 Answer (c) break even quality = fixed costs/(selling price - variable cost) rightarrow = 70000/(25 - 15) = 7000 unit Answer (d) TR = (P times Q) = (50 Q - 0.125 Q^2) MR = (d TR/dQ) = (50 - 0.25 Q) Now MC = MR rightarrow 50 - 0.25 Q = 15 rightarrow 35/0.25 = Q or Q = 140 unit Answer P = 50 - 0.125 (140) rightarrow P = $ 32.5 Answer The profit maximizing Q = 140 and P = $ 32.5