3. Given market demand Qd = 50 - P, and market supply P = Qs + 5
A) Find the market equilibrium price and quantity?
B) What would be the state of the market if market price was fixed at Birr 25 per unit?
C) Calculate and interpret price elasticity of demand at the equilibrium point.
4. What is the basic difference between cardinal and ordinal approaches of utility?
5. Elaborate the justifications for the negative slope and convexity of indifference curve�
A) To find the market equilibrium price and quantity, we need to set the demand equal to the supply.
Demand: Qd = 50 - P
Supply: P = Qs + 5
Setting Qd equal to Qs:
50 - P = Qs + 5
Adding P and subtracting 5 from both sides:
45 = Qs + P
Substituting supply (P = Qs + 5) into the equation:
45 = Qs + (Qs + 5)
Combining like terms:
45 = 2Qs + 5
Subtracting 5 from both sides:
40 = 2Qs
Dividing by 2:
Qs = 20
Substituting Qs = 20 into the supply equation (P = Qs + 5):
P = 20 + 5
P = 25
Therefore, the market equilibrium price is 25 and the market equilibrium quantity is 20.
B) If the market price was fixed at Birr 25 per unit, the market would be in equilibrium because this price matches the equilibrium price we found in part A.
C) To calculate the price elasticity of demand at the equilibrium point, we need to use the formula:
Elasticity = (% change in quantity demanded / % change in price)
At the equilibrium point, the quantity demanded and price are fixed. Any change in price would cause a movement away from the equilibrium point.
Since the price and quantity demanded are fixed at the equilibrium point, the price elasticity of demand would be zero. This means that a change in price does not affect the quantity demanded at the equilibrium point.
4. The basic difference between the cardinal and ordinal approaches of utility is as follows:
- Cardinal approach: This approach assumes that utility can be measured numerically and assigned specific values. Utility is considered as a quantitative concept, allowing for comparisons between levels of utility. It assumes that individuals can make precise judgments about the satisfaction they derive from consuming different goods or services. For example, an individual may say that they derive 10 units of utility from consuming a particular good.
- Ordinal approach: This approach only focuses on the ranking or ordering of preferences in terms of utility. It does not assign specific numerical values to utility. Instead, individuals are only assumed to be able to rank different goods or services in terms of which they prefer more or less. For example, an individual may say that they prefer good A over good B, but they do not assign any specific numerical value to this preference.
5. The negative slope of an indifference curve reflects the principle of diminishing marginal rate of substitution. It means that as an individual consumes more of one good, they are willing to give up less and less of the other good to maintain the same level of satisfaction.
The convexity of an indifference curve reflects the principle of diminishing marginal utility. It means that as an individual consumes more of one good, the additional level of satisfaction they derive from each additional unit of that good decreases. In other words, the more of a good someone already has, the less they value each additional unit of that good.
These concepts of diminishing marginal rate of substitution and diminishing marginal utility explain the negative slope and convexity of indifference curves.