Question

PA1

Using the graph below, develop a two- to four-page response in APA format using the following
three-question prompt:

Question 1
What is the maximum amount you would pay for an asset that generates an income of $250,000
at the end of each of five years if the opportunity cost of using funds is 8%?

Question 2
Suppose the supply function for product X is given by Qxs = −30 + 2Px − 4Pz.

● How much of product X is produced when Px = $600 and Pz = $60?
● How much of product X is produced when Px = $80 and Pz = $60?
● Suppose Pz = $60. Determine the supply function and inverse supply function for good
X. Graph the inverse supply function.

Question 3
Suppose the own price elasticity of demand for a good X is −5, its income elasticity is −1, its
advertising elasticity is 4, and the cross-price elasticity of demand between it and good Y is 3.

Determine how much the consumption of this good will change if:

● The price of good X decreases by 6%.
● The price of good Y increases by 7%.
● Advertising decreases by 2%.
● Income increases by 3%.

Question 4
● A consumer is in equilibrium at point A in the accompanying figure. The price of good X
is $5.

● What is the price of good Y?
● What is the consumer’s income?
● At point A, how many units of good X does the consumer purchase?
● Suppose the budget line changes so that the consumer achieves a new equilibrium at
point B. What change in the economic environment led to this new equilibrium? Is the
consumer positively or negatively affected by the price change?

Answer 1

Question 1:

To determine the maximum amount you would pay for an asset that generates an income of $250,000 at the end of each of five years, we can use the concept of present value. The present value of future cash flows can be calculated by discounting them at the opportunity cost of using funds, which in this case is 8%.

Using the formula for present value of an annuity, we can calculate the maximum amount you would pay:

PV = C * [(1 - (1 + r)^(-n)) / r]

Where:

PV = Present value

C = Cash flow per period ($250,000)

r = Discount rate (8% or 0.08)

n = Number of periods (5 years)

Plugging in the values:

PV = $250,000 * [(1 - (1 + 0.08)^(-5)) / 0.08]

PV ≈ $943,448.34

Therefore, the maximum amount you would pay for the asset is approximately $943,448.34.

Question 2:

a) When Px = $600 and Pz = $60, we can substitute these values into the supply function for product X:

Qxs = -30 + 2Px - 4Pz

Qxs = -30 + 2($600) - 4($60)

Qxs = -30 + 1200 - 240

Qxs = 930

Therefore, when Px = $600 and Pz = $60, the quantity of product X produced is 930 units.

b) When Px = $80 and Pz = $60:

Qxs = -30 + 2Px - 4Pz

Qxs = -30 + 2($80) - 4($60)

Qxs = -30 + 160 - 240

Qxs = -110

Since the quantity cannot be negative, we assume that no product X is produced when Px = $80 and Pz = $60.

c) When Pz = $60, the supply function for good X is:

Qxs = -30 + 2Px - 4($60)

Qxs = -30 + 2Px - 240

Qxs = 2Px - 270

The inverse supply function is obtained by solving for Px:

Px = (Qxs + 270) / 2

To graph the inverse supply function, plot Px on the vertical axis and Qxs on the horizontal axis. The equation Px = (Qxs + 270) / 2 represents the slope-intercept form of a linear equation, where the slope is 2 and the y-intercept is 270.

Question 3:

a) If the price of good X decreases by 6%, the quantity demanded will change by the own price elasticity of demand. The percentage change in quantity demanded is given by:

Percentage change in quantity demanded = Elasticity * Percentage change in price

Change in quantity demanded = -5 * (-6%) = 30%

Therefore, the consumption of good X will increase by 30% if the price of good X decreases by 6%.

b) If the price of good Y increases by 7%, the quantity demanded of good X will change by the cross-price elasticity of demand. The percentage change in quantity demanded is given by:

Percentage change in quantity demanded = Elasticity * Percentage change in price

Change in quantity demanded = 3 * 7% = 21%

Therefore, the consumption of good X will decrease by 21% if the price of good Y increases by 7%.

c) If advertising decreases by 2%, the quantity demanded of good X will change by the advertising elasticity. The percentage change in quantity demanded is given by:

Percentage change in quantity demanded = Elasticity * Percentage change in advertising

Change in quantity demanded = 4 * (-2%) = -8%

Therefore, the consumption of good X will decrease by 8% if advertising decreases by 2%.

d) If income increases by 3%, the quantity demanded of good X will change by the income elasticity. The percentage change in quantity demanded is given by:

Percentage change in quantity demanded = Elasticity * Percentage change in income

Change in quantity demanded = -1 * 3% = -3%

Therefore, the consumption of good X will decrease by 3% if income increases by 3%.

Question 4:

Unfortunately, you mentioned an accompanying figure, but I cannot see or refer to any images as I am a text-based AI model. If you can provide a description of the figure or provide the relevant information in text format, I will be happy to assist you further with your question.

Step-by-step explanation: