Please answer all of a, b, and c The lumber industry (lumber is wood used in man

Question

Please answer all of a, b, and c

The lumber industry (lumber is wood used in manufacturing) in a city is a perfectly competitive industry. The longrun cost function for a lumber firm is C(q)=10q^2 +1000 where q is a standardized amount of lumber. The market demand in the city is Q=10,00020*P.

a. Find the longrun equilibrium market price and quantity of lumber. How many firms will be in the market?

b. The government decides to impose a perunit quantity tax of t=50 on the suppliers; if a firm sells one unit they must pay 50 to the government. Find the shortrun equilibrium price and quantity after the tax is imposed. What is the profit of each firm? Note: to keep things simple, assume an individual firm’s longrun marginal cost is the same as their shortrun marginal cost.

c. Now find the new longrun equilibrium price and quantity with the tax. How many lumber firms will be in the market? Draw a diagram comparing the equilibrium price and quantity in the three situations: 1) before the tax 2) the shortrun after the tax 3) the longrun after the tax.  

Explanation / Answer

a) In a long-run equilibrium, ATC equals Marginal Cost and profits equal zero. Setting the two equations equal:
10q+1000/q = 20q
=> q= 10
However, the question wants us to find long run prices also. We know that the firm produces were Price = Marginal Revenue(MR) = Marginal Cost(MC), so if we can determine the firm’s MC, then we can determine the equilibrium price in the market.
We know that:
MC = 20q
And solved for:
q = 10
Substituting:
MC = 20(10) = 200
The equilibrium price in the market is 200.
Now we should determine the market quantity Q from the market demand curve, given that we know the market price is 200. Market demand is given as:
Q = 10000-20P
And we know that market price = 200, so:
Q = 10000-20(200)
Q = 6000
Since each firm is making 10 units, there must be 300 firms, since they are all identically sized.

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