Question

The economist for the Grand Corporation has estimated the company's cost function, us-

ing time series data, to be

TC = 50 + 16Q -20° + 0.20%

where TC = Total cost I

Q = Quantity produced per period

a. Plot this curve for quantities 1 to 10.

b. Calculate the average total cost. average variable cost, and marginal cost for these quan-

tities, and plot them on another graph.

c. Discuss your results in terms of decreasing, constant, and increasing marginal costs.

Does Grand's cost function illustrate all these?

Answer 1

$TC = 50 + 16Q - 2Q^2 + 0.2Q^3.$

a. This curve for quantities 1 to 10 is upward-sloping.

b. $ATC = TC/Q = 50/Q + 16 - 2Q + 0.2Q^2.$

$AVC = VC/Q = 16 - 2Q + 0.2Q^2.$

$MC = TC'(Q) = 16 - 4Q + 0.6Q^2.$

c. We can observe increasing marginal costs.