1. Sometimes firms conduct experiments where they temporarily change prices (thi
ID: 1194578 • Letter: 1
Question
1. Sometimes firms conduct experiments where they temporarily change prices (this may be done with selective coupons and other discounting methods) to see how the consumer responds to a price change. Let's assume that our firm charges $15 per unit of output and on average has 400 units sold per day. However, for the last week the firm offered a $5 discount and charged only $10 per unit of output. During the week of the discount the firm observed that the average daily sales were 1000 units.
(i) Given the price and quantity information, calculate the Elasticity of Demand for the product.
(ii) What type of good/service is this (inelastic, elastic, etc.)? Explain.
(iii) Interpret your elasticity calculation.
Bonus: Part (iv) and (v) are considered bonus.
(iv) If we operate under the assumption of ceteris paribus, what is the best linear representation of the demand faced by the firm [please provide the equation for the demand in terms of Q = f(P)]. Hint: This is just solving for the equation of the line…so solve for slope and intercept.
Recall that to get the equation of a line we can choose one point and note:
(Y – Y1) = M(X – X1) à in this case your point would be (X1, Y1) à (P,Q) where M = AQ / AP
(v) If we continue to operate under the assumption that the demand is linear, what prediction can you make about the firm's level of sales at the price of $8? Use your solution to predict this.
Explanation / Answer
We have:
Price (OLD) = $ 15
Price (NEW) = $ 10
Qty Demand(OLD) = 400
Qty Demand(NEW) = 1000
Calculating the Percentage Change in Quantity Demanded
[QDemand(NEW) - QDemand(OLD)] / QDemand(OLD)
[1000 - 400] /400 = (600/400) = 1.50
In percentage terms this would be 150.00 %
Calculating the Percentage Change in Price
[Price(NEW) - Price(OLD)] / Price(OLD)
[10 - 15] /15 = (-5/15) = - 0.3333
In percentage terms this would be -33.33 %
Price Elasticity of Demand = (% Change in Quantity Demanded)/(% Change in Price)
= 1.50/-0.333
= -4.50045
We will take absolute value and ignore the negative sign. Hence price elasticity of demand when the price of goods decrease from $ 15 to $ 10 is 4.50045.
Since Price elasticity of demand is greater than 1, Goods/Service is sensitive to price and Demand is price elastic.
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