Question:
Calculate the price elasticity of demand when the quantity demanded decreases from 100 units to 80 units as a result of a 20% increase in price.
Answer:
Question: A firm's total cost function is given as TC = 100 + 5Q + 0.1Q^2. Determine the average variable cost (AVC) and average total cost (ATC) when the quantity produced is 50 units.
Answer:
Average Variable Cost (AVC) = Variable Cost / Quantity = (5Q + 0.1Q^2) / Q = 5 + 0.1Q = 5 + 0.1(50) = 10
Average Total Cost (ATC) = Total Cost / Quantity = (100 + 5Q + 0.1Q^2) / Q = (100 + 5Q + 0.1Q^2) / 50 = 100/50 + 5/50Q + 0.1/50Q^2 = 2 + 0.1Q + 0.002Q^2 = 2 + 0.1(50) + 0.002(50^2) = 2 + 5 + 5 = 12
Question:
A perfectly competitive market has a market demand function given by Q = 2000 - 20P, where Q represents quantity and P represents price. The market supply function is given by Q = 1000 + 10P. Determine the equilibrium price and quantity in this market.
Answer:
To find the equilibrium price and quantity in a perfectly competitive market, we need to set the market demand equal to the market supply:
Market Demand: Q = 2000 - 20P
Market Supply: Q = 1000 + 10P
Setting these two equations equal to each other and solving for the equilibrium price (P):
2000 - 20P = 1000 + 10P
2000 - 1000 = 20P + 10P
1000 = 30P
P = 1000/30
P ≈ 33.33
Substituting the equilibrium price (P) into either the market demand or supply function to find the equilibrium quantity (Q):
Q = 2000 - 20P
Q = 2000 - 20(33.33)
Q ≈ 2000 - 666.6
Q ≈ 1333.4
Therefore, the equilibrium price in this market is approximately $33.33 and the equilibrium quantity is approximately 1333.4 units.