Thanks!! 21.The perfectly competitive market demand for a type of carpet known a
ID: 1134577 • Letter: T
Question
Thanks!! 21.The perfectly competitive market demand for a type of carpet known as KP-7 has been estimated as: P- 40-0.25Q, where P is price ($/yard) and Q is rate of sales (hundreds of yards per month). The market supply is expressed as: P-5.0+0.05Q A typical firm in this market has a total cost function given as: TC 100- 20.0q+2.0q2 a. Using the market demand and supply functions, determine the equilibrium market output and price. (3) b. How much output will a profit-maximizing perfectly competitive firm will produce and sell in this market? (2) c. Calculate the profit (or loss) earned by the typical firm. (2)Explanation / Answer
21.
A.
At equilibrium,
Market demand = Market supply
40-.25Q = 5+.05Q
.3Q = 35
Q = 35/.3 = 116.67 (hundreds of yard)
P = 5+ .05*(35/.3)
P = $10.83
B.
At profit maximizing level,
MR = MC
P = 40-.25Q
Or
Q*P = revenue = 40Q - .25Q^2 -------- (1)
Differentiation of equation 1 w.r.t. Q, will give marginal revenue MR.
MR = 40-.5Q
TC = 100-20Q + 2Q^2
MC = -20 + 4Q
40-.5Q = -20 + 4Q
60 = 4.5Q
Q = 60/4.5 = 13.33 (hundreds of yard)
C.
Profit earned by the firm = revenue – total cost
Profit earned by the firm = 13.33*10.83 - (100-20*13.33 + 2*13.33^2)
Profit earned by the firm = -$44.41
So, there is a loss of $44.41 to the firm.
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