You are a perfectly competitive firm and P = $5 . Your cost function is: C(Y )=

ID: 1201389 • Letter: Y

Question

You are a perfectly competitive firm and P = $5 . Your cost function is: C(Y )= Y2 + Y + 4

a)What are your firm’s variable costs? Fixed costs?

b)Write down your firm’s profit function.

c)Write down the firms first order condition for profit maximization and solve for Y * .

d)Show that at this production point, profit is maximized rather than minimized (sufficient

condition is met.)

e)Solve for the profit earned by the firm.

f)Should you produce Y * , or should you shut down and produce nothing? Explain why.

C(Y )= Y2 + Y + 4

a) Variable Cost = Y2 + Y as it depends on Y => 3.75 ( PLUGGING y = 1.5)

Fixed cost is independent of Production level and is 4.

b) P = $5 .

Total Revenue = P x Y => 5Y

Profit = TR - TC => 5Y - (Y2 + Y + 4) =>-Y2 + 4Y + 4

c) The firms first order condition for profit maximization and solve for Y * = MR = MC

For a perfectly competitive firm, MR is same as Price; MR =4

MC = dTC/ d Y => 2Y + 1

First Order Conditon; 2Y + 1 = 4 => Y = 3/2 = 1.5

d) Sufficient Condition = Second Order derivative OF cost should be positive implying positive slope of Mc

d2 TC / dY2 = 2 => CONDITION IS MET

E) TR = 5 X 1.5 => 7.5

TC = (1.5)2 + 1.5+ 4 => 7.75

PROFIT = TR- TC => - 0.25 I.E. FIRM IS MAKING LOSS

F) iT SHOULD NOT SHUT DOWN. Loss << TVC

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