A.). Short-run equilibrium output of a competitive firm is derived at the point where MR = MC.
The market equilibrium price for a competitive firm = MR
MR = 9
MC = Derivative of the Total Cost relative to quantity:
TC = 200 + Q + 0.02Q2
MC = "\\frac{\\partial TC} {\\partial Q} = 1 + 0.04Q"
Set MR = MC:
MR = MC
9 = 1 + 0.04Q
9 – 1 = 0.04Q
8 = 0.04Q
Q = "\\frac{8} {0.04} = 200"
Q = 200
The short-run equilibrium output of the firm = 200
Profit = TR – TC
TR = P x Q = 9 x 200 = 1,800
TC = 200 + 200 + 0.02(2002)
TC = 200 + 200 + 800 = 1,200
Profit = 1,800 – 1,200 = 600
The profit of the firm = 600
B.). The values of MC, ATC, and AVC are derived as follows:
Short-run equilibrium output (Q) = 200
MC = "\\frac{\\partial TC} {\\partial Q} = 1 + 0.04Q" = 1 + 0.04(200) = 1 + 8 = 9
MC = 9
ATC = "\\frac{TC}{Q} = \\frac{200 + Q + 0.02Q^{2} }{Q} = \\frac{200 + 200 + 0.02(200)^{2} }{200} = 1 + 1 +4 = 6"
ATC = 6
AVC = "\\frac{VC}{Q} = \\frac{ Q + 0.02Q^{2} }{Q} = \\frac{200 + 0.02(200)^{2} }{200} = 1 + 4 = 5"
AVC = 5
C.). Producer’s surplus at the equilibrium output:
Produce’s surplus = "\\frac{1}{2} (200\\times 9) = 0.5\\times 1800 = 900"
Produce’s surplus = 900
D.). Derive the output level that will make the profit of the firm zero:
Set MC = ATC
MC = 9
ATC = "\\frac{200}{Q} +0.02Q"
9 = "\\frac{200}{Q}" + 0.02Q
Multiply both sides by 100:
900 = "\\frac{20000}{Q}" + 2Q
Divide both sides by Q:
900Q = 20000 + 2Q2
900Q – 2Q2 – 20000 = 0
Q = 23
The output level that will make the profit of the firm zero = 23
Comments
Leave a comment