Question

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

ing time series data, to be where TC 5 Total cost

TC=50+16Q-2Q2 +0.2Q3 Q 5 Quantity produced per period

1. Plot this curve for quantities 1 to 10.
2. Calculate the average total cost, average variable cost, and marginal cost for these quan-
3. tities, and plot them on another graph.
4. Discuss your results in terms of decreasing, constant, and increasing marginal costs.
5. Does Grand’s cost function illustrate all these?

Answer 1

Solution:

1.). The graph for quantities 1 to 10 is as below:

2.). TC = 50 + 16Q – 2Q² + 0.2Q³

Average total cost (ATC) = $\frac{(50 + 16Q – 2Q^{2} + 0.2Q^{3} )}{Q} = \frac{50}{Q} + 16 - 2Q + 0.2Q ^{2}$

Average variable cost (AVC) = $\frac{(16Q – 2Q^{2} + 0.2Q^{3} )}{Q} = 16 - 2Q + 0.2Q ^{2}$

Marginal cost (MC) = 16 – 4Q + 0.6Q²

 

3.). The graph showing ATC, AVC, and MC is as below:

 

4.). If average costs are falling, marginal costs must be lower than average, and if average costs are rising, marginal costs must be higher than average. On its way up, the marginal cost must cut the cost curve at its lowest point.

 

5.). Grand’s cost function depicts decreasing, constant, and increasing marginal costs.