Calculate the market demand function.

Tangunu, let's knock this out. a) Determine the market demand and supply functions for fairly used Mercedes cars. Step 1: Calculate the market demand function. The individual demand function is Q_d = 52 - 2P, and there are 75 buyers. Q_MD = 75 × (52 - 2P) Q_MD = 3900 - 150P Step 2: Calculate the market supply function. The individual supply function is Q_s = 15 + 10P, and there are 10 sellers. Q_MS = 10 × (15 + 10P) Q_MS = 150 + 100P The market demand function is Q_MD = 3900 - 150P and the market supply function is Q_MS = 150 + 100P. b) Complete the market demand and supply schedule of fairly used Mercedes cars below. Step 1: Calculate Quantity Demanded (Q_MD) and Quantity Supplied (Q_MS) for each price using the functions from part (a). • For P = 5: Q_MD = 3900 - 150(5) = 3900 - 750 = 3150 units Q_MS = 150 + 100(5) = 150 + 500 = 650 units • For P = 10: Q_MD = 3900 - 150(10) = 3900 - 1500 = 2400 units Q_MS = 150 + 100(10) = 150 + 1000 = 1150 units • For P = 15: Q_MD = 3900 - 150(15) = 3900 - 2250 = 1650 units Q_MS = 150 + 100(15) = 150 + 1500 = 1650 units • For P = 20: Q_MD = 3900 - 150(20) = 3900 - 3000 = 900 units Q_MS = 150 + 100(20) = 150 + 2000 = 2150 units Step 2: Complete the schedule. | Price (FCFA) | 5 | 10 | 15 | 20 | |--------------|------|------|------|------| | Quantity demanded(units) | 3150 | 2400 | 1650 | 900 | | Quantity supplied(units) | 650 | 1150 | 1650 | 2150 | c) Using the market demand and supply functions obtained in a) above, determine: i) The equilibrium price ii) The equilibrium quantity Step 1: Set market demand equal to market supply to find the equilibrium price. Q_MD = Q_MS 3900 - 150P = 150 + 100P 3900 - 150 = 100P + 150P 3750 = 250P P = (3750)/(250) P = 15 The equilibrium price is 15 FCFA. Step 2: Substitute the equilibrium price into either the market demand or market supply function to find the equilibrium quantity. Using Q_MD: Q = 3900 - 150(15) Q = 3900 - 2250 Q = 1650 The equilibrium quantity is 1650 units. d) If the government fixes a minimum price of 20 FCFA for these cars, how much will it cost her to maintain the Price? Step 1: Calculate the quantity demanded and quantity supplied at the minimum price of 20 FCFA. At P = 20 FCFA: Q_MD = 3900 - 150(20) = 3900 - 3000 = 900 units Q_MS = 150 + 100(20) = 150 + 2000 = 2150 units Step 2: Determine the surplus quantity. Surplus = Q_MS - Q_MD = 2150 - 900 = 1250 units. Step 3: Calculate the cost to the government to maintain the price. Cost = Surplus quantity × Minimum price Cost = 1250 units × 20 FCFA/unit = 25000 FCFA The cost to