Suppose that the Acme Gumball Company has a fixed proportions production functio

Question

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. Have these curves in part (4) shifted?

Explanation / Answer

1. The cost function for producing 1000 gumballs per hour is

TC = 3r + 2w

This is because to produce 1000 gumballs, required 3 gumball presses and 2 workers.

And as r is hourly rent for gumball presses and w is hourly wage per worker, So the total cost is TC = 3r + 2w.

2. Now to produce any number of gumballs, total cost funtion will be

TC = q * (3r + 2w).

3. AC is average cost of production which is find by dividing total cost function by quantity q.

So, AC = (3r + 2w)

And marginal cost(MC) is found by diiferentiating total cost function.

So, MC =  (3r + 2w).

4. When r = 2 and w = 3,

then AC = MC = 12.

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