Question

1. (a-g 4% each; h-I 7% each) An economist estimated that the Total Cost function is TC = $100 + 30Q + 20Q2 where Q is the number of widgets produced. Also, the marginal cost is calculated as follows: MC = $30 + 40Q Based on this information, determine the following for producing 10 units of output:

Average Total Costs= $_______________ Marginal Cost= $_______________ Assume the firm produces 10 units of output and that it will shut down if it does not generate enough revenue to at least cover its variable costs. What is the shutdown price per widget? $_______________ Assume the firm produces 10 units of output. What is the breakeven price (that is, at what market price per widget would total revenue equal total cost)? $_______________

Answer 1

Total Cost function is TC = $100 + 30Q + 20Q2 and marginal cost is MC = $30 + 40Q.

Average total cost is ATC = TC/Q or 100/Q + 30 + 20Q.

At 10 units of output, we have

Average Total Costs ATC = 100/10 + 30 + 20*10 = 240

Marginal Cost = 30 + 40*10 = 430

Now variable cost is VC = 30Q + 20Q^2 and AVC = VC/Q = 30 + 20Q. Shut down price is minimum of AVC which is $30 (when Q is 0). Hence, the shutdown price per widget is $30.

Assume the firm produces 10 units of output. Break-even price is equal to the ATC at this level of output. We see that ATC is $240 when Q is 10 units. Hence break even price is $240.