Calculate the price elasticity of demand for a good when its price increases from $10 to $12 and the quantity demanded decreases from 100 to 80 units.
Suppose the market demand and supply curves for a good are given by Qd = 500 - 2P and Qs = 3P - 100. Find the equilibrium price and quantity.
A firm has total fixed costs of $1000 and variable costs of $5 per unit. Calculate the firm’s average total cost when it produces 100 units.
Suppose a consumer has an income of $1000 and can buy two goods: X and Y. The price of X is $10 per unit and the price of Y is $20 per unit. Draw the consumer’s budget constraint.
Ответы
Ответ:
To calculate the price elasticity of demand, we use the formula:
Price Elasticity of Demand = (% change in quantity demanded) / (% change in price)
The % change in quantity demanded is:
((100-80)/100) * 100 = 20%
The % change in price is:
((12-10)/10) * 100 = 20%
Therefore, the price elasticity of demand is:
20% / 20% = 1
To find the equilibrium price and quantity, we need to set the quantity demanded equal to the quantity supplied:
500 - 2P = 3P - 100
Solving for P, we get:
5P = 600
P = 120
Substituting P back into either the demand or supply equation, we get the equilibrium quantity:
Q = 500 - 2(120)
Q = 260
Therefore, the equilibrium price is $120 and the equilibrium quantity is 260 units.
The average total cost (ATC) of producing 100 units is:
ATC = (Total Fixed Cost + Total Variable Cost) / Quantity
ATC = ($1000 + ($5 * 100)) / 100
ATC = $15
To draw the consumer's budget constraint, we need to calculate the maximum quantities of X and Y that the consumer can afford given their income and the prices of the two goods. The budget constraint is a straight line with a slope equal to the ratio of the prices of X and Y (-10/20 = -1/2) and intercepts on the X and Y axes equal to the quantities of X and Y that the consumer can afford with their income ($1000).
At a price of $10 per unit for X and $20 per unit for Y, the consumer can afford:
100 units of X (100 * $10 = $1000)
50 units of Y (50 * $20 = $1000)
Therefore, the budget constraint is a line that goes through the points (100,0) and (0,50), with an equation of:
10X + 20Y = 1000
We can plot this line on a graph with X on the horizontal axis and Y on the vertical axis, and shade the area below the line to represent the combinations of X and Y that the consumer can afford. Any point on the line represents a combination of X and Y that exhausts the consumer's budget