Question

Note: don't copy paste answer again and again its my 3rd attempt and each time same picture of answers uploaded i need the actual answers of the following question

Problem:

      Suppose that the demand for Cod Liver Oil (CLO) can be written Q_D =5000-2P (so, the inverse demand curve for CLO is P=2500-0.5Q_D), where P is the price per ton (in dollars) of CLO and Q_D is the quantity demanded (in tons) in a period.

1. Use Excel Scatterplots to draw (i) the demand curve and (ii) the corresponding total revenue curve for this market (in two separate diagrams).
2. Calculate price elasticity of demand (using the point elasticity formula) at the following amounts of CLO along this demand curve: Q_D=4000, Q_D =2500, Q_D =1000.
3. Calculate total revenue from sales in this market at each of these quantities: Q_D=4000, Q_D =2500, Q_D =1000.
4. Assume that demand will decrease based on a parallel shift of the demand curve. Explain what will happen to elasticity at Q_D=2500 (will it increase or decrease and why?). What will happen to total revenue at this quantity (will it increase or decrease and why?). Will the maximum total revenue for the market be achieved at a greater or a smaller quantity than Q_D=2500?

Answer 1

a) Using Excel, the following diagrams have been drawn:
i) the demand curve:

ii) the total revenue curve:

b) The value of point elasticity of demand is given by the ratio of percentage change in quantity demanded to the percentage change in price. Applying that formula, we get the following values of price elasticity:
Qd = 4000  
( with point elasticity approach two points are needed on the demand curve so unable to calculate elasticity for first point)
Qd = 2500 Ep = 1
Qd = 1000 Ep =0.25

c) Revenue from sales are as follows
Qd = 4000 P = 500 Therefore , Total revenue = 4000 x 500 = 2,000,000
Qd = 2500 P = 1250 Therefor , Total revenue = 2500 x 1250 = 3125000
Qd = 1000 P = 2000 therefore , Total revenue = 2000 x 1000 = 2,000,000

d) When Qd = 2500, P = 1250
When the demand decreases based on a parallel shift of the demand curve, it means that there is a decrease in demand due to factors other than its own price. When this parallel shift occurs it means that for a change in price, the slopes will remain same and so the percentage changes in price and quantity will be same but the initial level of quantity will fall. As this is in the denominator, the value of elasticity will rise in turn. So value of elasticity will rise.Total revenue will fall as due to the decrease in demand, the quantity demanded at the given price will fall and thus the total expenditure will also decrease.

Demand curve : P= 2500 - 0.5Qd
or, TR = 2500Qd - 0.5Qd^2
In order to maximize Total revenue, we differentiate with respect to Qd and equate to 0 ( standard maximization technique)

MR = 2500 - Qd = 0
Or, Qd* = 2500
So total revenue is maximized when Qd = 2500. So Total revenue will not be maximized at a greater or a smaller quantity of Qd but at Qd= 2500 exactly.