The Johnson Robot Company\'s marketing officials report to the company\'s CEO th

Question

The Johnson Robot Company's marketing officials report to the company's CEO that the demand curve for the company's robots is P = 600 - 4Q, where P is the price of a robot, and Q the number sold per month.

1. Derive the marginal revenue curve for the firm.

Total revenue = P x Q

(600 - 4Q) * Q = 600Q – 4Q^2

Marginal Revenue = dTR/dQ

D[(600Q – 4Q^2)/dQ = 600 – 8Q

(not sure if the above is right?)

2. If the firm wants to maximize its dollar sales volume, what price should it charge?

3. What is the price elasticity of demand when P = $100

4. At what prices is the demand for the firm's product price elastic versus inelastic?

5. What can you say about the income elasticity of demand for robots? Why?

Explanation / Answer

Ans 1. Your calculation is correct. Marginal Revenue is an addition to the total revenue by selling one additional unit of good. This can be calculated by finding the first derivative of the total revenue with respect to the quantity.

Total revenue

= P x Q where P = 600-4Q

=(600 - 4Q) * Q

= 600Q – 4Q^2

Marginal Revenue

= dTR/dQ

        = D[(600Q – 4Q^2)/dQ

       = 600 – 8Q

Ans 2. To maximize the dollar sales value/revenue Marginal Revenue (MR) should be equal to zero.

So, 600-8Q = 0

Or Q = 75.

Substituting the value of Q in equation

P = 600-4Q = 600-4*75 = 300

So the Price should be 300 and the Quantity should be 75.

Ans 3. Price Elasticity of Demand is a measure of the responsiveness of the quantity demanded to a change in price.

Using the same equation P= 600-4Q

Or                                     Q= (600-P)/4

Or                                     dQ/dP = -1/4

Now price elasticity of demand when P = 100

Substituting the value of P in the equation

Q = (600-P)/4 = 500/4 = 125

Therefore Elasticity of demand

= % change in Quantity / % change in Price               

= -1/4*100/125

= -1/5

= -0.2

As the value is less than 1, demand is inelastic when P = 100.

Ans4. When the price is high and the quantity is less then the demand is elastic. Suppose the quantity is 10, then Price is 560,

So elasticity = -1/4*560/10

                     = -14 Highly Elastic      

Ans 5: Unrelated question. Please post it as separate question

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