Market for slim mobiles is represented by the following functions
(A)Q+1/3P= 36, Q+9=1/2 P (B) Q=4P2-4P , Q=44-3P2
Required
i)Identify the demand and supply functions. Give reasons for your answer
ii) Find the equilibrium price and quantity
b)If supply of fuel increased by 12% due o 540 increase in aggregate prices. Calculate elasticity of supply and suggest ways of stabilizing the supply of fuel in Kenya.
c) Suppose the market demand and market supply for a commodity are given as follows:
Qd = 100-2p
Qs = 4 + 4p
i) Determine the equilibrium price and quantity for the market.
d)Suppose the maximum price is fixed at $20. Illustrate the effect of this price control on a supply and demand diagram. Is there a shortage? If so, what is the excess demand?
e) The popularity of brown ‘chapatis’ causes consumers’ tastes to shift away from bread. Show the effect of this shift on the market demand for blue band, which is used mainly when people eat toast
i) To identify the demand and supply functions in the given market, we need to analyze the equations and determine which one represents demand and which one represents supply.
Looking at the equations:
(A) Q + 1/3P = 36
and
Q + 9 = 1/2P
(B) Q = 4P^2 - 4P
and
Q = 44 - 3P^2
For demand, we usually observe a negative relationship between price and quantity. In equation (A), we see that as P increases, Q decreases, indicating an inverse relationship. Therefore, equation (A) represents the demand function.
For supply, we usually expect a positive relationship between price and quantity. In equation (B), the relationship between P and Q is not clear from the given form. However, if we rearrange equation (B) to solve for P, we get P = (Q + 4) / (2Q). As the quantity supplied (Q) increases, the price (P) also increases, indicating a positive relationship. Therefore, equation (B) represents the supply function.
ii) To find the equilibrium price and quantity, we need to set the demand and supply functions equal to each other and solve for P and Q.
Setting Q + 1/3P = 36 equal to Q = 4P^2 - 4P, we can solve for P and Q using algebraic manipulation:
Q + 1/3P = 36
Substitute Q with 4P^2 - 4P:
4P^2 - 4P + 1/3P = 36
4P^2 - 3 11/3P = 36
4P^2 - (33/3)P = 36
4P^2 - 11P = 36
Simplifying further, we get a quadratic equation:
4P^2 - 11P - 36 = 0
Solving this equation will give us the equilibrium price (P) and corresponding equilibrium quantity (Q).
b) To calculate the elasticity of supply, we need to know the percentage change in quantity supplied relative to the percentage change in price.
Given that supply of fuel increased by 12% and aggregate prices increased by $540, we can calculate the elasticity of supply.
Elasticity of supply = Percentage change in quantity supplied / Percentage change in price
= (12% / $540) * 100
To suggest ways of stabilizing the supply of fuel in Kenya, we would need more information about the specific factors affecting supply and the market conditions.
c) To determine the equilibrium price and quantity for the market, we need to set the market demand and market supply functions equal to each other and solve for P and Q.
Qd = 100 - 2p (Demand function)
Qs = 4 + 4p (Supply function)
Equating the demand and supply functions:
100 - 2p = 4 + 4p
Solving this equation will give us the equilibrium price (P) and corresponding equilibrium quantity (Q).
d) If the maximum price is fixed at $20, it acts as a price ceiling in the market. To illustrate the effect of this price control on a supply and demand diagram, we can plot the demand and supply curves and identify the equilibrium point.
With the maximum price set at $20, the price is below the equilibrium price. This will lead to excess demand or a shortage in the market. On the diagram, the demand curve will intersect the supply curve to the left of the equilibrium point. The distance between the quantity demanded and quantity supplied at this price will represent the excess demand.
e) A change in consumer tastes, such as the popularity of brown 'chapatis' shifting away from bread, will cause a shift in the market demand for blue band. This shift in demand will result in a change in the quantity demanded at each price level.
On a demand and supply diagram, the market demand curve will shift to the left, indicating a decrease in demand for blue band due to the shift in consumer tastes. The new equilibrium point will be determined by the intersection of the shifted demand curve and the original supply curve, indicating the new equilibrium price and quantity for blue band.