Question

1- DHL Company specializes in rapid parcel delivery. Cross sectional data from DHL’s regional hub in Palestine were used to estimate the demand equation for the company’s services. Holding income and prices of other goods constant, the demand equation is estimated to be

P = 66Q -1 /3

where P is the price per pound and Q is pounds delivered. The marginal cost of delivery is constant and equal to $2 per pound.

a. What is the point-price elasticity of demand?

b. What are the profit-maximizing price and quantity?

c. What are the total revenue maximizing price and quantity?

Answer 1

a. The demand equation faced by DHL company for its parcel delivery is given as P=66Q-1/3 or P=66Q-0.33 approximately, where P and Q represent the price per pound and the quantity or weight of parcels delivered measured in pounds. The marginal cost of delivery incurred by the company or MC is $2 per pound.

Now, based on the demand function when the Q is 10, the price per pound of parcels become:

P=66Q-0.33

P=66*(10)-0.33

P=660-0.33

P=659.67

Again based on the demand function given, when Q=20, the price per pound of parcels becomes:

P=66Q-0.33

P=66*(15)-0.33

P=990-0.33

P=989.67

Therefore, the percentage change in Q due to the change in P based on the calculations performed above=(15-10)/10=1/2=0.5 and the percentage change in P=(989.67-659.67)/659.67=0.5 approximately.

Therefore, the point elasticity of demand, in this case=0.5/0.5=1

b. Now, assuming a monopoly market for courier services and based on the profit-maximizing condition of a single or monopolistic firm in this case, the firm will produce the output which corresponds to the equality between the marginal revenue of production and the marginal cost of production incurred by the firm. The total revenue of the company or TR=P*Q=(66Q-0.33)*Q=66Q^2-0.33Q and the marginal revenue of the company or TR=dTR/dQ=132Q-0.33.

Therefore, based on the profit-maximizing condition of any competitive firm, we can state:-

MR=MC

132Q-0.33=2

132Q=2+0.33

132Q=2.33

Q=2.33/132

Q=0.0177 approximately

The profit-maximizing quantity of output or parcels of the company would be 0.0177 pounds.

Now, plugging the profit-maximizing quantity of the company into the demand function, we get:-

P=66Q-0.33

P=66*(0.0177)-0.33

P=1.1682-0.33

P=0.8382

The profit-maximizing per pound price charged by DHL company for the parcels is $0.8382

c) The total revenue of the company or TR=66Q^2-0.33Q and the marginal revenue of the company or MR=132Q-0.33. Now, based on the revenue-maximizing condition of any firm, the marginal revenue has to be set equal to 0.

Hence, based on the revenue-maximizing condition, it can be stated:-

MR=0

132Q-0.33=0

132Q=0.33

Q=0.33/132

Q=0.0025

Therefore, the revenue-maximizing quantity of parcels of the company is 0.0025 pounds

Now, plugging the revenue-maximizing quantity of parcels into the demand function, we get:-

P=66Q-0.33

P=66*(0.0025)-0.33

P=0.165-0.33

P=-0.165

The revenue-maximizing per pound price of parcels and the quantity of parcels of the DHL company are $-0.165 and 0.0025 pounds respectively.