Please Show All Work For The Questions 4 The Following Relat

Please Show All Work For The Questions4 The Following Relations Descr

Please show all work for the questions 4. The following relations describe monthly demand and supply for a computer support service catering to small businesses. QD=3,000−10P, QS=−1,000+10P where Q is the number of businesses that need services and P is the monthly fee, in dollars. a. At what average monthly fee would demand equal zero? b. At what average monthly fee would supply equal zero? c. Plot the supply and demand curves. d. What is the equilibrium price/output level? e. Suppose demand increases and leads to a new demand curve: QD=3,500−10P. What is the effect on supply? What are the new equilibrium P and Q? f. Suppose new suppliers enter the market due to the increase in demand so the new supply curve is Q=−500+10P. What are the new equilibrium price and equilibrium quantity? Show these changes on the graph.

Paper For Above instruction

The analysis of market equilibrium involves understanding the relationships between demand and supply curves, and how shifts in these curves affect equilibrium prices and quantities. The given problem provides specific demand and supply equations for a computer support service catering to small businesses, which serve as a basis for this analysis.

Initially, the demand curve is represented by the equation QD = 3,000 − 10P, and the supply curve by QS = −1,000 + 10P, where Q is the quantity demanded or supplied, and P is the price in dollars.

Part A: Zero Demand Price

To find the price at which demand equals zero, set QD to zero and solve for P:

0 = 3,000 − 10P

10P = 3,000

P = 300

Thus, at a monthly fee of $300, demand would be zero, indicating no businesses would seek services at or above this price.

Part B: Zero Supply Price

For supply to be zero, set QS to zero:

0 = −1,000 + 10P

10P = 1,000

P = 100

Hence, when the price is $100, suppliers would be willing to supply zero units, implying suppliers are not willing to offer services below this fee.

Part C: Plotting the Demand and Supply Curves

The demand curve is a straight line declining from high demand at low prices to zero demand at $300, while the supply curve rises from zero at $100. Typically, plotting these functions involves creating axes with P (price) on the vertical and Q (quantity) on the horizontal. The intersection point of these lines, which determines equilibrium, can be identified visually or via calculation.

Part D: Equilibrium Price and Quantity

To find the equilibrium, set demand equal to supply:

3,000 − 10P = −1,000 + 10P

3,000 + 1,000 = 10P + 10P

4,000 = 20P

P = 200

Substitute P back into either equation to find Q:

QD = 3,000 − 10(200) = 3,000 − 2,000 = 1,000

or

QS = −1,000 + 10(200) = −1,000 + 2,000 = 1,000

Therefore, the equilibrium price is $200, and the equilibrium quantity is 1,000 businesses.

Part E: Effect of Increased Demand

The new demand curve becomes QD = 3,500 − 10P. This shift illustrates increased demand at every price point, leading to a higher demand for services. The supply remains unchanged. To find the new equilibrium:

Set the new demand equal to the original supply:

3,500 − 10P = −1,000 + 10P

3,500 + 1,000 = 10P + 10P

4,500 = 20P

P = 225

Calculating the new quantity:

QD = 3,500 − 10(225) = 3,500 − 2,250 = 1,250

Thus, increased demand raises the equilibrium price to $225 and the quantity to 1,250 businesses.

Part F: Entry of New Suppliers

The new supply curve is QS = −500 + 10P. To determine the new equilibrium, set the new demand and supply equations equal:

3,500 − 10P = −500 + 10P

3,500 + 500 = 10P + 10P

4,000 = 20P

P = 200

Substitute P into either equation for Q:

QD = 3,500 − 10(200) = 3,500 − 2,000 = 1,500

or

QS = −500 + 10(200) = −500 + 2,000 = 1,500

The new equilibrium price is lower at $200, with an increased quantity of 1,500 businesses, indicating that new suppliers have increased market capacity, leading to a higher quantity at the same price level as initially.

Conclusion

The dynamics of supply and demand illustrate how equilibrium prices and quantities respond to shifts in market conditions. In this case, increased demand and the entry of new suppliers significantly affect market outcomes, mirroring economic principles such as upward and downward pressure on prices and quantities. Graphical analysis consolidates these findings, emphasizing the importance of curve shifts in understanding market equilibrium.

References

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