Please help me with this question.?

Question

A perfectly competitive firm has short-run total variable costs given by SVC = q2 and short-run total fixed costs of FC = $4. Derive this firm’s seven short-run cost curves. Calculate output and profits if the price were P = $8.00. Explain whether this firm should shutdown if price falls to P = $2.00. Provide a labelled diagram for SRMC, SRATC, SRAFC and SRAVC.

The only confusing part is the SVC=q2, does that mean that the short run average VC =2 and Marginal cost=0?????

What will the output be? and how will the curvs look like?

Answer 1

There should not be any confusion.  SVC=q2 = q squared =q^2 is the shortrun total variable cost . So the average variable cost is total variable cost divided by quantity of output q. Thus the Average VC is given SVC/q= q^2/q= q. The marginal cost (MC) is found by differentiating SVC with respect to q and thus MC= d(SVC)/dq= 2q

What will the output be?

Since it is a perfectly competitive firm. It will, in order to maximise profits, should choose that level of output q at which MC= MR= Price = P

So, 2q = 8 or q= 4.

Its total revenue would be P*q= $8*4= $32.

As against this the firm' total cost for producing would be equal to Fixed cost + total Variable Cost= $4+q^2= $4+ $ 4^2= $4+$16= $20.

So, the firm makes a profit of $(32-20)= $12 So why should the firm shut down- it should continue with the business and earn profits.

If the price falls to $2, MC=MR= P gives 2q=2 or q=1.

Profit equals P*q -(FC+total Variable Cost )= $2*1- ($4+q)= $2 - ($4+$1)= $2-$5 = - $3. The company makes a loss, but it does cover its total variable cost: P=$2 > total Variable cost = $q = $1. So it earns a contribution towards part recovery of fixed cost.. It should not shut down immediately and see if the over a period of time it can recover the full Fixed costs.

Answer 2

STC=SFC+SVC=4+Q^2

Answ: STC=4+Q^2 (this is Short-run cost curve)

MC=(STC)'=2Q

P=8=MR

TR=8*Q

Profit maximization condition MR=MC

MR=8

MC=2Q

8=2Q

Q=8/2=4

Profit=TR-TC=8Q-4-2Q= 6Q-4

Q=4

Profit=6*4-4=24-4=20

Answ: Profit=20 Output=4

If P=2 them MR=2

MR=MC

MR=2

MC=2Q

2=2Q

Q=1

SVC=Q^2=1^2=1

TR=Q*P=1*2=2

Since VC<TR then firm should continue production

MC=(STC)'=2Q

SRATC=SRTC/Q=(4+Q^2)/Q= 4/Q+Q

SRAFC=SRFC/Q=4/Q

SRAVC=SRVC/Q=Q^2/Q=Q