Question

The economist for the Grand Corporation has estimated the company’s cost function, using time series data, to be TC = 50 + 16Q - 2Q2 + 0.2Q3 where TC = Total cost Q = Quantity produced per period

i. Calculate the average total cost, average variable cost, and marginal cost for these quantities.

ii. Discuss your results in terms of decreasing, constant, and increasing marginal costs. Does Grand’s cost function illustrate all these?

Answer 1

Answer (1) TC = 50+16Q+2Q²+0.2Q³

ATC = 50/Q+16+2Q+0.2Q²

VC = 16Q+2Q²+0.2Q³

AVC= 16+ 2Q+0.2Q²

MC = 16+4Q+0.6 Q²

Answer 2 : Increasing marginal cost means with increase an additional unit of output the cost has been increasing at rapid speed. This point when Output are producing at initial level where as after somepoint marginal cost start decreasing and when business has been flourished properly than marginal cost of producing an additional unit remain constant.

When at initial level quantity the grand corporation faces increasing marginal cost but as the production increases the marginal cost has been start increases .Therefore, this shows that grand corporation faces increasing marginal cost function

At Q = 2 units

MC = 16+4×2+0.6×2×2 = 24.4

Where as at Q = 3 units

MC = 16+4×3+0.6×3×3 = 33.4

This shows grand corporation has increasing marginal cost function.