Question

Alexandria has her own lawn service. It takes her two hours to cut a lawn and she cuts 1,000 lawns per year. She uses solar-powered equipment (truck and mower) that will last forever – and can be sold at any time for $30,000. Alexandria could earn $12 per hour as a swim instructor. The interest rate is 10 percent.

1. Given her current level of output, compute her marginal cost and average cost of cutting lawns.
2. Suppose she decrease the number of lawns cut to 500 lawns per year. Now compute her marginal cost and average cost of cutting lawns.

Evaluate the following statement. If the total variable cost of production is the sum of the marginal cost of each additional unit of output, we can calculate the marginal cost by taking the total variable cost of production and dividing it by the quantity.

Suppose the total cost of producing 10,000 tennis balls is $40,000, and the fixed cost is $10,000.

1. When output is 10,000 what are the average variable cost and average total cost?
2. Is the dollar difference between the average variable cost and average total cost greater when output is 10,000 or 30,000? Explain your reasoning.

Answer 1

solution:

Given (a)Total cost $40,000

(b) Fixed cost is $10,000

(c) quantity is 10,000 tennis balls

therefore, total variable cost is 40,000 - 10,000 = $30,000 (total cost - fixed cost)

Average variable cost = Total variable cost / quantity   

= 30,000 / 10,000

= $3

Average total cost = Total cost / quantity

= 40,000 / 10,000

= $4

Dollar difference between average variable cost and average total cost = 4 - 3 = $1 ------- (i)

New assumption: Quantity is 30,000$Therefore, Total cost = 1,20,000 (30,000 x 4 - quantity x average total cost)

Fixed cost remains he same at $ 10,000

Total variable cost = $ 1,10,000(1,20,000 - 10,000 - Total cost - fixed cost)

Average variable cost = $ 3.7 (1,10,000 / 30,000 - total variable cost / quantity)

Average total cost = $ 4 (1,20,000 / 30,000 - total cost / quantity)

Dollar difference between average variable cost and average total cost = 4 - 3.7 = $ 0.3 ----------- (ii)

Answer: Dollar difference between average variable cost and average total cost is greater when the output is 10,000 units

--------- from (i)