Consider A Competitive Market For A Good

Consider A Competitive Market For A Good

Consider a competitive market for a good where the demand curve is determined by the demand function: P=10-2QD and the supply curve is determined by the supply function: P=1+QS. What is the quantity demanded of the good when the price level is P = $4?

What is the quantity supplied of the good when the price level is P = $4?

At P=$4 there is: a. Competitive equilibrium in the market; b. Excess supply in the market; c. Excess demand in the market; d. Rationing in the market;

What is the value of the price elasticity of demand if the price of the good changes from Po=$4 to Pi=$5?

What is the value of the price elasticity of supply if the price of the good changes from Po=$4 to Pi=$5?

What is the equilibrium quantity level for the good in the competitive market?

What is the equilibrium price level for the good in the competitive market?

What is the consumer surplus in the competitive market?

What is the producer surplus in the competitive market?

What is the total surplus in the competitive market?

For Questions 11-15, assume a market intervention of the form of price floor. The price floor is set at P=$6. This price floor is binding, so it has an impact on the equilibrium of the economy. How many units of the good the producers are willing to supply the market at the considered market intervention?

How many units of the good the consumers are willing to demand the market at the considered market intervention?

How many units of the good are going to be sold in the market at the considered market intervention?

What is the value of the Consumer Surplus considering this market intervention?

What is the value of the Producer Surplus considering this market intervention?

For Questions 16-20, assume a market intervention of the form of a $3 per unit tax on the consumption of the good. How many units of the good are sold in the market at equilibrium considering this market intervention?

How much are consumers going to pay per unit of the good under this market intervention?

How much is the per unit amount that producers will receive as payment under this market intervention?

How much are the tax revenues under this market intervention?

How much is the Dead Weight Loss under this market intervention?

Paper For Above instruction

The market dynamics of supply and demand are fundamental to understanding how prices and quantities are determined in a competitive market. This analysis focuses on a specific market with given demand and supply functions, examining equilibrium, elasticities, surpluses, and the effects of government interventions such as price floors and taxes.

Market Equilibrium and Quantities at a Given Price

The demand function, P = 10 - 2QD, indicates that as the quantity demanded increases, the price decreases. To find the quantity demanded when the price is $4, we substitute P = 4 into the demand function:

4 = 10 - 2QD → 2QD = 10 - 4 → 2QD = 6 → QD = 3 units.

Similarly, the supply function P = 1 + QS implies that at P = 4, supply is:

4 = 1 + QS → QS = 3 units.

Since quantity demanded equals quantity supplied at P = 4, the market clears at this price, indicating a competitive equilibrium with a quantity of 3 units.

Market Equilibrium and Elasticity Calculations

Given the equilibrium quantity of 3 units at P = 4, we analyze how demand and supply respond to price changes to determine price elasticities.

The price elasticity of demand (PED) measures the responsiveness of quantity demanded to price changes and is calculated as:

PED = (ΔQD / QD) / (ΔP / P) = (Change in quantity demanded / initial quantity demanded) divided by (Change in price / initial price).

Taking the demand function, the derivative with respect to P is -2, meaning for a 1-unit increase in P, QD decreases by 0.5 units. Using the midpoint (arc elasticity) formula between P = 4 and P = 5:

Q at P = 4: QD = (10 - 4) / 2 = 3 units; at P = 5: QD = (10 - 5) / 2 = 2.5 units.

Change in QD = 2.5 - 3 = -0.5, change in P = 5 - 4 = 1, initial QD = 3, initial P = 4.

Thus, PED = (-0.5 / 3) / (1 / 4) = (-0.1667) / 0.25 = -0.6668.

This indicates that demand is inelastic with respect to price changes around this point.

Similarly, the price elasticity of supply (PES) is derived from the supply function where the derivative is 1. The change in quantity supplied when price increases from $4 to $5 is:

Q at P = 4: QS = 3 units; at P = 5: QS = 4 units.

Change in QS = 1, initial QS = 3, ΔP = 1.

PES = (1 / 3) / (1 / 4) = 0.333 / 0.25 = 1.333.

The supply is elastic in this range, responding significantly to price changes.

Market Equilibrium Quantities and Surpluses

The equilibrium quantity remains 3 units, and the equilibrium price is $4. Consumer surplus (CS) is the area above the price and below the demand curve, calculated as:

CS = 0.5 (Maximum price consumers are willing to pay - equilibrium price) equilibrium quantity.

The maximum price consumers are willing to pay is the intercept of demand at QD=0: P = 10.

CS = 0.5 (10 - 4) 3 = 0.5 6 3 = 9.

Producer surplus (PS) is the area below the price and above the supply curve, found by integrating the supply curve from zero to equilibrium quantity:

PS = (Price - Supply intercept) * quantity / 2, or directly by calculating the area of a triangle with height (4 - 1) = 3 and base = 3:

PS = 0.5 3 3 = 4.5.

Total surplus (TS) combines CS and PS:

TS = 9 + 4.5 = 13.5.

Impact of Market Interventions: Price Floor

Setting a binding price floor at P = $6 exceeds the equilibrium price of $4, leading to surplus. At P = 6, the quantity producers are willing to supply is:

QS = 6 - 1 = 5 units.

Consumers are willing to demand:

QDs = (10 - 6) / 2 = 2 units.

Since QD

The consumer surplus decreases because consumers buy less at a higher price, calculated as:

CS = 0.5 (Maximum willingness to pay - P_floor) quantity sold = 0.5 (10 - 6) 2 = 4.

The producer surplus increases as producers are willing to sell more at the higher price, but since only 2 units are sold, the producer surplus is:

PS = (P_floor - supply intercept) quantity sold / 2 = 0.5 (6 - 1) * 2 = 5.

Market Intervention: Per-Unit Tax

Introducing a $3 per-unit tax shifts the supply curve upward by $3, effectively reducing the quantity sold. To find the new equilibrium, the demand equals the new supply:

Original demand: P = 10 - 2QD

Original supply: P = 1 + QS

New supply with tax: P = 1 + QS + 3

Set demand equal to the new supply: 10 - 2Q = 1 + Q + 3 → 10 - 2Q = 4 + Q → 10 - 4 = 3Q → 6 = 3Q → Q = 2 units.

The price consumers pay remains from the demand function:

At Q = 2, P = 10 - 2*2 = 10 - 4 = 6.

Producers receive the price minus the tax: 6 - 3 = 3 per unit.

The total tax revenue is:

Tax per unit quantity sold = $3 2 = $6.

Deadweight loss arises from the reduction in traded quantity, leading to lost surplus:

Deadweight loss is calculated as the area of the triangle between the original and new quantities, which is 0.5 tax (original quantity - new quantity) = 0.5 3 (3 - 2) = 1.5.

This analysis illustrates the effects of market interventions on market outcomes, demonstrating changes in quantity, prices paid and received, surpluses, government revenue, and overall efficiency.

Conclusion

Analyzing a competitive market with specific demand and supply functions reveals the fundamental mechanics of equilibrium, elasticities, and surpluses. When external interventions like price floors and taxes are introduced, they distort market equilibrium, leading to surpluses, reduced consumer and producer surpluses, and efficiency losses. These findings emphasize the importance of understanding market responses to policies to make informed economic decisions that balance efficiency and fairness.

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