Answer and Explanation:
The computation of Output level is shown below:-
The equilibrium condition of competitive firms will be
P = MC
70 = 0.009q^2 + 50
0.009q^2 = 70 - 50
0.009q^2 = 20
q^2 = 20 ÷ 0.009
q^2 = 2,222.222222
So,
q = 47.14045208
or
= 47.14
The computation of profit per unit is shown below:-
Total profit = Total sales - Total cost
= ($70 × 47.14) - (0.003q^3 + 50q + 750)
= $3299.8 - {0.003 (47.14)^3 + 50 × 47.14 + 500}
= -$121.460639032
or
= -$121.46
Profit per unit = Total profit ÷ Output
= -$121.46 ÷ 47.14
= -$2.58
The computation of Produce or shutdown is shown below:-
Total variable cost (TVC) = 0.003q^3 + 50q
= 0.003 (47.14)^3 + 50 × 47.14
= 2671.260639
or
= 2,671.26
AVC = Total cost ÷ Output
= 2,671.26 ÷ 47.14
= 56.66652524
or
= 56.67
Here, $70 which is the market price is higher than AVC that is 56.67, so the company will produce
The firm will realize an economic loss in the long run. If the situation will not modify, this firm will shut down.
In the short term, the company can deliver as its marginal income exceeds the marginal cost. Yet in the long run, the company would suffer an economic loss because the average income per unit is smaller than the average expense per unit. But it would suffer a loss in the long run, but then would prefer to shut down.