M2A1: Market Forces: Demand and Supply and Quantitative Demand Analysis

M2A1: Market Forces: Demand and Supply and Quantitative Demand Analysis

M2A1: Market Forces: Demand and Supply and Quantitative Demand Analysis

6. Suppose demand and supply are given by Q^d = 60 – P and Q^s = P -20

1. What are the equilibrium quantity and price in this market?

EQ Price Equation: Q^d = Q^s  à  60 – P = P – 20 à 60 + 20 + P + P à 2P = 80 à P = $40

EQ Quantity Equation: Q^d = 60 – P à Q^d = 60 – 40 = 20 à Q^s =P – 20 à Q^s = 40 – 20 = 20

Answer: EQ Price is $40, and EQ Quantity is 20 Units.

• Determine the quantity demanded, the quantity suppled, and the magnitude of the surplus if a price floor of $50 is imposed in this market.

Quantity Demanded Equation:  Q^d = 60 – P à Q^d = 60 – 50 = 10 Units

Quantity Supplied Equation: Q^s = P – 20 à Q^s = 50 – 20 = 30 Units

Surplus Equation: Surplus Quantity = quantity supplied at $50 – quantity demanded at $50

30 – 10 = 20 Units à Price floor ($50) * 20 Units = $1,000

Answer: Quantity Demanded (10), Quantity Suppled (30), and the magnitude of the surplus (20 Units) Total: $ 1,000

• Determine the quantity demanded, the quantity suppled, and the magnitude of the shortage if a price celling of $32 is imposed in this market. Also determine the full economic price paid by consumers.

Quantity Demanded Equation:  Q^d = 60 – P à Q^d = 60 – 32 = 28 Units

Quantity Supplied Equation: Q^s = P – 20 à Q^s = 32 – 20 = 12 Units

Shortage Equation: Shortage Quantity = $32 = 60-P – 12 = 48

28 – 12 = 16 Units à Price floor ($32) * 16 Units = $512

Full Economic Price = Price Ceiling + (Full Economic Price – Price Ceiling)

32 + (48 – 32) = 32 + 16 = $48

Answer: Quantity Demanded (28), Quantity Suppled (12), and the magnitude of the shortage (16 Units) Total: $ 512.  Full Economic Price Paid by consumers ($48).

7. Suppose demand and supply are given by Qdx=14-1/2Px and Qsx=1/4Px-1

2020
		E
4
0		4

a. Determine the equilibrium price and quantity.  Show the equilibrium graphically.

Qdx = Qsx à 14-0.5Px = 0.25Px-1 à 0.75Px = 15 à Px = $20

Qdx = 14 – 0.5Px à 14 – 0.5 (20) = 4 Units

Answer: Equilibrium Price ($20) and Quantity (4)       

b. Suppose a $12 excise tax is imposed on the good. Determine the new equilibrium price and quantity.

Answer:

c. How much tax revenue does the government earn from the $12 tax?

Answer:

2. Using regression analysis on the data from a field experiment, set demand curve for a product is estimated to be Qdx=1,200-3Px-0.1Pz, where Pz=300

a. What is the own price elasticity of demand when Px=$140 Is demand elastic or inelastic at this price?  What would happen to the firm’s Revenue if you decided to change a price below $140?

Answer:

b. What is the own price elasticity of demand when Px=$240 Is demand elastic or inelastic at this price?  What would happen to the firm’s Revenue if you decided to change a price above $240?

Answer:

c. What is the cross-price elasticity of demand between good X and good Z when Px=$140?  Are goods X and Z substitutes or complements?

M2A1: Market Forces: Demand and Supply and Quantitative Demand Analysis