Question a):

 

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

Given the total cost function:

• TC=50+16Q−2Q2+0.2Q3TC=50+16Q−2Q2+0.2Q3

The marginal cost is equal to:

• MC=ΔTCΔQ=16−4Q+0.6Q2MC=ΔTCΔQ=16−4Q+0.6Q2

The average total cost is equal to:

• ATC=TCQ=50Q+16−2Q+0.2Q2ATC=TCQ=50Q+16−2Q+0.2Q2

From the total cost function, the variable cost is equal to:

• VC=16Q−2Q2+0.2Q3VC=16Q−2Q2+0.2Q3

And the average variable cost is equal to:

• AVC=VCQ=16−2Q+0.2Q2AVC=VCQ=16−2Q+0.2Q2

 

Question b)

 

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

Grand's total cost function has increasing, decreasing and constant marginal cost.

Given the marginal cost in part (a), the marginal cost will be decreasing if the slope of the marginal cost with respect to the output is negative. If the slope is positive, then the marginal cost is increasing and if the slope is constant, then the cost function has constant marginal costs.

• ΔMCΔQ=−4+1.2QΔMCΔQ=−4+1.2Q

For decreasing marginal costs:

• ΔMCΔQ=−4+1.2Q<0ΔMCΔQ=−4+1.2Q<0

• Q<103Q<103

Therefore, the marginal cost will be increasing for all output levels less than 10/3.

For constant marginal cost:

• ΔMCΔQ=−4+1.2Q=0ΔMCΔQ=−4+1.2Q=0

• Q=103Q=103

Thus, the firm will have a constant marginal cost at Q = 10/3.

For increasing marginal cost:

• ΔMCΔQ=−4+1.2Q>0ΔMCΔQ=−4+1.2Q>0

• Q>103Q>103

The firm will have increasing marginal cost for output levels above Q = 10/3.