Question

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.

Answer 1

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

Answer 2

To calculate the price elasticity of demand, we use the formula:

E = (ΔQd / Qd) / (ΔP / P)

Where: ΔQd = Change in quantity demanded = Q2 - Q1 Qd = Initial quantity demanded = Q1 ΔP = Change in price = P2 - P1 P = Initial price = P1

Given: Initial price (P1) = $10 Final price (P2) = $12 Initial quantity demanded (Q1) = 100 Final quantity demanded (Q2) = 80

ΔQd = Q2 - Q1 = 80 - 100 = -20 ΔP = P2 - P1 = 12 - 10 = 2

Using the formula, we can calculate the price elasticity of demand:

E = (-20 / 100) / (2 / 10) = (-0.2) / (0.2) = -1

The price elasticity of demand for the good is -1, which indicates that the demand for the good is elastic.

Now, let's find the equilibrium price and quantity using the given demand and supply curves:

Demand: Qd = 500 - 2P Supply: Qs = 3P - 100

Equilibrium occurs when Qd = Qs, so we can set the demand and supply equations equal to each other:

500 - 2P = 3P - 100

Simplifying the equation:

5P = 600 P = 600 / 5 P = 120

Substituting the equilibrium price (P = 120) into the demand or supply equation:

Qd = 500 - 2P Qd = 500 - 2(120) Qd = 500 - 240 Qd = 260

The equilibrium price is $120, and the equilibrium quantity is 260 units.

Next, let's calculate the firm's average total cost (ATC) when it produces 100 units. Given:

Total fixed costs (TFC) = $1000 Variable costs per unit (VC) = $5 Quantity produced (Q) = 100

The average total cost (ATC) is given by the formula:

ATC = (TFC + TVC) / Q

TVC = VC * Q TVC = $5 * 100 TVC = $500

ATC = ($1000 + $500) / 100 ATC = $1500 / 100 ATC = $15

The firm's average total cost when it produces 100 units is $15.

Lastly, let's draw the consumer's budget constraint. The consumer's income is $1000, and the prices of goods X and Y are $10 and $20 per unit, respectively.

Let's assume the consumer can buy a maximum of x units of good X and y units of good Y.

The budget constraint is given by the equation:

Px * x + Py * y = Income

Substituting the given values:

$10 * x + $20 * y = $1000

To draw the budget constraint, we need to determine the feasible combinations of x and y. Let's solve the equation for various values of x and y:

For x = 0: $10 * 0 + $20 * y = $1000 $20y = $1000 y = $1000 / $20 y = 50

For y = 0: $10 * x + $20 * 0 = $1000 $10x = $1000 x = $1000