Question

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Answer 1

a) Variable cost is one which changes with change in number of goods sold here good is 'treehouse rentals' . It is that part of the total cost which depends on quantity sold. When quantity sold = 0, VC = 0. In the total cost function given , 45000 is the amount which is spent irrespective of number of treehouse rented. Whereas the remaining part depends on Q which is number of treehouse rented .

Variable cost VC = 500Q - 20Q² + (1/2)Q^{​​​​​​3}

b) Fixed cost is more obvious for such a firm . Fixed cost would be the cost that firm would incur in construction of treehouse and in buying furnitures etc. Fixed cost is the cost which the firm has to incur even if none of its treehouse gets a rent.

But the variable cost is the cost which the firm incurrs when it the treehouse gets rented . Variable cost is incurred with each treehouse rented out to tenant ,i.e., as Q increases. Such cost would be cost of electricity and water which would be zero if none of the treehouse is rented. Since it's a luxurious product, the treehouse is company may offer utilities such as internet, food , regular cleaning of the rented treehouse , in some cas fuel for cooking. These constitutes the variable costs.

c)Marginal cost = d(total cost)/dQ = d( 45000 + 500Q -20Q^​2+ (1/2)Q^{​​​​​​3} ) /dQ = 500-40Q + (3/2)Q^{​​​​​​2}​​​​​

d) Q = 10, VC = 500(10)-20*(10)² +(1/2)(10)³ = 5000-2000+500 = $3500

e) Q = 5 , MC = 500- 40*5 + (3/2)(5)² = 500 - 200+ 37.5 = $ 337.5

f ) Average cost = total cost/Q = 45000/Q + 500 -20Q + (1/2)Q^{​​​​​​2}​​​​​