Question 3 Suppose that the Acme Gumball Company has a fixed proportions product

Question

Question 3

Suppose that the Acme Gumball Company has a fixed proportions production function that requires it to use three gumball presses and two workers to produce 1000 gumballs per hours. Please find the cost per hour of producing 1000 gumballs. (Suppose r is the hourly rent for gumball presses and w is the hourly wage.) Assume Acme can produce any number of gumballs they want using this technology. Please find the total cost function in this case. (Suppose q is output of gumballs per hour, measured in thousands of gumballs.) Please find the average and marginal cost of gumball production (again, measure output in thousands of gumballs). Please graph the average and marginal cost curves for gumballs assuming r=2, w=3. Now graph these curves for r = 3, w = 3. Now graph these curves for r = 3, w = 3. Have these curves in part (4) shifted?

Explanation / Answer

1.

Cost per hour = Gumball rent + Workers’ wages

                        = 3 × r + 2 × w

                        = 3r + 2w

2.

Number of hours = q / 1,000

Total cost (TC) = (3r + 2w) × (q/1,000)

3.

Average cost = TC/q

                        = {(3r + 2w) × (q/1,000)} ÷ q

                        = (3r + 2w) ÷ 1,000

Marginal cost = Derivative of TC with respect of q

                        = (3r + 2w) ÷ 1,000

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