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Consider a perfectly competitive firm selling hats qd(p) = 200-P market supply qs(p) = 50+ 4P....

Consider a perfectly competitive firm selling hats qd(p) = 200-P market supply qs(p) = 50+ 4P. What is the equilibrium price for these hats?

If a hat company has a cost function of c(q) =20 + 1/3q2  what would their profit maximizing number of hats be that they should produce. Please show all steps.

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Market is in equilibrium when Quantity demand = quantity supplied i.e. qd(p) = qs(p) and equilibrium price is that price at which qd(p) = qs(p)

Now, qd(p) = qs(p)

=>200 - P = 50 + 4P

=> P = 30

Hence, the equilibrium price for these hats is 30.

Perfect competitive firms are price taker and hence charges price per unit set by a market for any number of quantity and hence because of this Demand faced by a competitive firm is perfect elastic(horizontal) and because of this P = MR(Marginal revenue) for perfect competitive firm.

In order to maximize profit a perfect competitive firm produces that quantity at which P = MC

Here P = 30 calculated above

MC = Marginal Cost = dc/dq = (2/3)q

P = MC

=> 30 = (2/3)q

=> q = 45

Hence, their profit maximizing number of hats be that they should produce is 45 hats

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