Question

Minnesota Wave Rentals incurs a marginal cost of $48 per day of providing a WaveRunner to a tourist. Minnesota Wave Rentals has daily fixed costs of $8,000. The daily demand curve facing Minnesota Wave Rentals is P = 240 – 0.10*Q, with Q representing the number of WaveRunners rented, and P representing the price-to-rent rate charged to tourists.

Show your explanations and math in the spaces below (typed), or if you use Excel, please state your results in the spaces below, and refer to your uploaded Excel file.

a)What is the profit-maximizing price to rent a WaveRunner? How many WaveRunners will Minnesota Wave Rentals rent per day? What are Minnesota Wave Rentals’ daily total revenues, total costs, and total profits?

b) If Minnesota Wave Rentals’ marginal cost increases to $60 per day due to a tax on each personal watercraft rental to support state tourism advertising, what would be the profit-maximizing price to rent and quantity rented?

c) If, instead, Minnesota Wave Rentals’ fixed costs change, to $10,000 per day, due to higher dock fees all over Minnesota, what would be the profit-maximizing price to rent and quantity rented?

d) Use marginal analysis to explain the difference in how Minnesota Wave Rentals should respond to increased marginal cost vs. increased fixed cost.

Answer 1

Total cost for Minnesota = 48Q + 8000

where Q is the no. of wave runner rented.

Total Revenue = 240Q- 0.10Q2

a. At profit maximizing level,

= TR - TC

or, = 192 - 0.20Q =0

or Q = 960

at this level of Q, P = 240 - 0.10(960) = $144

At profit maximising level of Q (no. of wave runner rented ) =960 and P(price to rent ratio) = $144,

Total Revenue= 240 x 960 - 0.10 ( 9602) = $138240

Total costs = 48(960) + 8000 = $38080

Total Profits = $138240 - $38080 = $100160

b. When marginal cost increases to $60 due to tax on each personal watercraft rental to support state tourism advertising then,

Total cost = 60Q +8000

So profit maximising level of Q is at -

= 180 - 0.20Q =0

therefore now Q = 900 and P = 240 - 0.10(900) = $150

c. If instead Minnesota Wave Rentals’ fixed costs change, to $10,000 due to higher dock fees all over Minnesota assuming every thing else constant then,

Total cost = 48Q +10000

at profit maximising level of Q is at -

= 192 - 0.20Q =0

therefore now Q = 960 and P = 240 - 0.10(960) = $144

Therefore increase in fixed cost does not change profit maximising level of output and price.

d. In marginal analysis we are considering incremental costs when variable or fixed cost change. If net benefit is positive then business operations should continue.

	Total Revenue	Incremental cost or change in cost	Net benefit
When variable cost rises to $60 from $48	900 x 150 = $135000	12 x 900=10800	124200
When Fixed cost rises to $10000	960 x 144= $138240	10000	$128240