The market for crayons has the following demand and supply curves: Qd = 25 - P Q
ID: 1197729 • Letter: T
Question
The market for crayons has the following demand and supply curves: Qd = 25 - P Qs = - 3 + 3P Find the equilibrium price and equilibrium quantity transacted in this market Consider a demand shock that keeps the price of this commodity at $3.50. Would this create a condition of excess demand or excess supply? How much would this "excess" be if in fact it does exist? Suppose the adoption of a new technology improves the efficiency of producing this commodity by 2 units, discuss the impact on the equilibrium values established in part (a) of this question (d) Assume that a shift in consumer preferences increased the consumption of this commodity by two units (prior to the induced technological innovation) how would this effect equilibrium price and equilibrium quantity transacted?Explanation / Answer
Soln :
a) Demand function
Qd = 25 - P2
Qs = - 3 + 3P
At equilibrium
Qd = Qs
25 - P2 = - 3 + 3P
P2 + 3P -28 = 0
P2 + 7P - 4P -28 = 0
P(P+7) - 4( P+7) = 0
P = $ 4 [ equilibrium price]
Qd = 25 - 16
Q = 9 [ Equilibrium quantity ]
b) If the price of the commodity is kept at $ 3.50
Qd = 25 - P2
Qd = 25 - 3.50 2
Qd = 12.75 units
Qs = - 3 + 3P
Qs = 8.25 units
Setting a price of $ 3.50 creates a condition of excess demand and this excess demand will be of the order of = (12.75 - 8.25 ) units
Excess demand = 4.5 units
C) If new technology improves the efficiency of producing this commodity by 2 units , the Quantity demanded = 9 units and the Quantity supplied = 11 units
Qs = -3 + 3P
11 = -3 + 3P
P = $ 4.66
The equilibrium price established by part a = $ 4
The technological efficiency will push the prices up by an amount = $ 4.66 - 4 ( $ 0.66)
d) If a shift in consumer preference increased the consumption of this commodity by 2 units
Qd = 25 - P2
11 = 25 - P2
P = $ 3.74
The equilibrium price established by part a = $ 4 and the new price will be = $ 3.74
The price is reduced by an amount = $ 4 - $ 3.74 ( $ 0.258)
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