(Advanced Analysis) Currently, at a price of $0.5 each, 100 popsicles are sold p

Question

(Advanced Analysis) Currently, at a price of $0.5 each, 100 popsicles are sold per day in the perpetually hot town of Rostin. Consider the elasticity of supply. In the short run, a price increase from $0.5 to $1 is unit-elastic (Es = 1). In the long run, a price increase from $0.5 to $1 has an elasticity of supply of 1.5. (Hint: Apply the midpoints approach to the elasticity of supply.)



How many popsicles will be sold/supplied each day in the short run if the price rises to $1 each?

      per day



How many popsicles will be sold/supplied per day in the long run if the price rises to $1 each?

Explanation / Answer

In the short run, a price increase from $0.5 to $1 is unit-elastic (Es = 1)

elasticity = % change in quantity/ % change in price

% change in quantity = 1 * % change in price

% change in quantity = (1-0.5)/(0.5+1)/2 = .67

change in quantity/ quantity = .67

let x be the new quantity

x-100 = 2/3*(x+100)/2

2/3x = 4/3*100

x = 200

In the long run, a price increase from $0.5 to $1 has an elasticity of supply of 1.5

elasticity = % change in quantity/ % change in price

% change in quantity = 1.5 * % change in price

% change in quantity = 1.5*(1-0.5)/(0.5+1)/2 = 3/2*2/3 =1

change in quantity/ quantity = 1

let x be the new quantity

x-100 = 1*(x+100)/2

x = 300

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