Question

1. There is a fruit seller who has 30 Kgs of apples to be sold and he wants to fix a price so that all the apples are sold. There are three customers in the market and their individual demand functions are given below:
D1=25-.05P
D2=20-.025P
D3=15-.075P
Where D is the demand and P is the price

Answer 1

Answer on Question #55274, Economics / Finance

1. There is a fruit seller who has 30 Kgs of apples to be sold and he wants to fix a price so that all the apples are sold. There are three customers in the market and their individual demand functions are given below:

D1=25-.05P

D2=20-.025P

D3=15-.075P

Where D is the demand and P is the price.

Solution:

Market demand represents the sum of the individual demand. Thus, the market demand function for the fruit seller will be equal to:

$$D_m = D_1 + D_2 + D_3$$

Now, we can substitute the individual demand functions in accordance with the condition of the task:

$$D_m = (25 - 0.05P) + (20 - 0.025P) + (15 - 0.075P)$$

We simplify the obtained equation:

$$D_m = (25 + 20 + 15) - (0.05P + 0.025P + 0.075) = 60 - 0.15P$$

It is known that the fruit seller wants to fix a price and to sell all apples; in this case, the total amount of apples is 30 Kgs and the price must be set so that market demand is for 30 Kgs of apples will be:

$$60 - 0.15P = 30$$

Now, we need to solve the equation for the price. We add -60 to both sides of the equation:

$$-0.15P = 30 - 60$$

Then, we divide both sides of the equation by -0.15:

$$-0.15P = -30$$ $$P = \$200$$

Thus, $200 is priced, at which fruit seller can sell all the apples. Consequently, we can determine the individual demands:

$$D_1 = 25 - 0.05P = 25 - (0.05 \cdot \$200) = 25 - 10 = 15 \text{ (units)}$$ $$D _ {2} = 2 0 - 0. 0 2 5 P = 2 0 - (0. 0 2 5 \cdot \$ 2 0 0) = 2 0 - 5 = 1 5 \text{ (units)}$$ $$D _ {3} = 1 5 - 0. 0 7 5 P = 1 5 - (0. 0 7 5 \cdot \$ 2 0 0) = 1 5 - 1 5 = 0 \text{ (units)}$$

Thus, the demand of each of the three buyers is:

$$D _ {1} = 1 5 \text{ units}, D _ {2} = 1 5 \text{ units and } D _ {3} = 0 \text{ units}.$$

http://www.AssignmentExpert.com/