Respuesta :
Answer:
Fixed cost = constant term i.e 50
Variable cost = [tex]\frac{q^2}{2}[/tex]
Explanation:
Data provided in the question:
Total Cost: TC = [tex]50+\frac{q^2}{2}[/tex]
here q is an individual firm's quantity produced
Demand QD = 160 − 4P
here P is the price and Q is the total quantity of the good
Now,
The Total cost = Fixed cost + Variable cost
here, Fixed is constant, while the variable cost varies with number of quantities being produced
Thus,
from the total cost function, we have
Fixed cost = constant term i.e 50
Variable cost = [tex]\frac{q^2}{2}[/tex]
Variable costs are short-run costs that alter in response to changes in a product's output. These costs are zero if output is zero.
[tex]\text{Total Cost (TC) = Fixed Cost (FC) + Variable Cost (VC)}[/tex]
[tex]\text{TC}=50+\frac{1}{2} q^2[/tex]
[tex]\text{As per the given TC equation;}\\\text{Fixed cost = 50}[/tex]
[tex]\text{Variable cost =}[/tex] [tex]\text{Q}^{2} / 2[/tex]
If P > = 10, the firm will stay in the market and produce in the long run (min ATC, firm will make zero or positive profits)
[tex]\text{In the short run:}\\\text{Firms = 6}\\\text{For individual firm : P = MC = q}\\\text{Total supply = 6 x q = Qs}\\[/tex]
[tex]\text{Qs = 6P}\\\text{Demand = 160 - 4P}[/tex]
Equating both:
[tex]\text{P = 16 (equilibrium price)}\\\text{Q = 96 (equilibrium quantity)}[/tex]
[tex]\text{Each firm produces= 96/6} \\= 1\text{6 units}[/tex]
[tex]\text{Each firm makes a profit of} =[/tex][tex]\text{P}[/tex] × [tex]\text{Q}[/tex][tex]- 50 - \frac{Q^{2} }{2}[/tex]
[tex]= 256 - 50 - \frac{162}{2} \\= 78[/tex]
- Firms are motivated to enter the market (positive profits)
The equilibrium price in the long run is $ 10 (= min ATC), and the total amount produced is [tex]160 - 4[/tex] × [tex]10 = 120 \text{units}[/tex]
In the market, there are [tex]= \frac{120}{10} = 12[/tex] enterprises, each producing [tex]10 \text{units (q = 10} \text{where ATC} = $ 10, \text{zero economic profit)}[/tex]
For more information related to the computation of costs, refer to the link:
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