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Marlene Aguilar
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The market demand for a type of carpet known as KS-12 has been estimated as
P = 75 - 1.5Q,
where P is price ($/yard), and Q is output per time period (thousands of yards per month). The market supply is expressed as P = 25 + 0.50Q. A typical competitive firm that markets this type of carpet has a marginal cost of production of
MC = 2.5 + 10q.
a. Determine the market equilibrium price for this type of carpet. Also determine the production rate in the market.
b. Determine how much the typical firm will produce per week at the equilibrium price.
c. If all firms had the same cost structure, how many firms would compete at the equilibrium price computed in (a) above?
d. Determine the producer surplus the typical firm has under the conditions described above. (Hint: Note that the marginal cost function is linear.)
P = 75 - 1.5Q,
where P is price ($/yard), and Q is output per time period (thousands of yards per month). The market supply is expressed as P = 25 + 0.50Q. A typical competitive firm that markets this type of carpet has a marginal cost of production of
MC = 2.5 + 10q.
a. Determine the market equilibrium price for this type of carpet. Also determine the production rate in the market.
b. Determine how much the typical firm will produce per week at the equilibrium price.
c. If all firms had the same cost structure, how many firms would compete at the equilibrium price computed in (a) above?
d. Determine the producer surplus the typical firm has under the conditions described above. (Hint: Note that the marginal cost function is linear.)
On Sep 22, 2024
a.Market equilibrium price is found by equating S and d.75 - 1.5Q = 25 + 0.50Q
50 = 2Q
Q = 25 (thousand yards per month)
The equilibrium selling price is
P = 75 - 1.5(25) = $37.5/yard.b.Since the firm's supply is based on its MC curve, we can use MC to determine production rate.P = 37.5 = MC = 2.5 + 10q
q =
= 3.5 (thousand yards / month)
c.Since each firm produces 3.5 thousand yards per month and total production is at 25 thousand yards per month, a total of 7.14 firms would be needed.d.Producer surplus is the area between the price of $37.5 and MC, bounded by zero and 3.5 units of output for the typical firm. The bounded area is a triangle.Area =
b ∙ h = (0.5)(3.5)(37.5 - 2.5) = $61.25 (thousand)
50 = 2Q
Q = 25 (thousand yards per month)
The equilibrium selling price is
P = 75 - 1.5(25) = $37.5/yard.b.Since the firm's supply is based on its MC curve, we can use MC to determine production rate.P = 37.5 = MC = 2.5 + 10q
q =
= 3.5 (thousand yards / month)c.Since each firm produces 3.5 thousand yards per month and total production is at 25 thousand yards per month, a total of 7.14 firms would be needed.d.Producer surplus is the area between the price of $37.5 and MC, bounded by zero and 3.5 units of output for the typical firm. The bounded area is a triangle.Area =
b ∙ h = (0.5)(3.5)(37.5 - 2.5) = $61.25 (thousand)