Question

With the snow season fast approaching us, Jack Frost, age 15, is considering his income-generating alternatives. Jack runs a snow removal business. He employs his friends at $10.00 per hour to clear sidewalks and driveways for neighbors, family friends, and fellow townsfolk. Last year, he had ten regular customers whose walks were shoveled 14 times each over the course of the winter. All told, Jack paid his friends $2,100 for their work for him this winter. Jack is considering the purchase of a used snowblower, which he believes will reduce the amount of time it takes his crew to complete a job to only 45 minutes. The snowblower will cost $1,176 (and will probably be worthless after one year of use), and will consume about $0.50 worth of gasoline and oil per use (per snow removal job). Given that Jack had no fixed costs, what was Jack's total cost function for last year?a. TC = 15Q b. TC = 100 c. TC = 11760 d. TC=0.5Q

Answer 1

a. TC = 15Q

Step-by-step explanation:

The cost function must include all the costs incurred by a business. Generally it includes a variable part and a fixed part. In this case, since Jack had no fixed costs, his costs are only variable: labor = $10 per hour

in total, Jack's business shoveled 10 x 14 = 140 walks, since he paid his friends $2,100 in total, the variable cost of shoveling one walk = $2,100 / 140 = $15

that means that last years cost function = $15 x number of walks shoveled, or

TC = 15Q (where Q is the number of walks shoveled)