1 A. “There is a direct relationship between marginal revenue (MR) and price elasticity” Discuss!
In order to provide the right prices for both goods and services, price elasticity is used to predict marginal revenue. Price elasticity describes what happens to the demand of a product as its price changes while demand rises as price falls and vice versa. For e.g. Elastic can be big screen TV’s while inelastic can be gasoline.
Marginal revenue is the additional revenue a company earns by selling more unit of a good or service. The relationship is that they work hand in hand as if a product has a high elasticity then lowering the price by even a little will increase demand a lot. This in turn makes the marginal revenue more lucrative.
Marginal revenue is then increased based on the price elasticity while indicating what a firm is able to produce (quantity of output) in order to maximize profit because the firm is unable to maximize profit in an inelastic range.
If demand is elastic, then marginal revenue is positive
If demand if inelastic, then Marginal revenue is negative
If demand is unit elastic , then marginal revenue is zero
Best Purchase demand function is Q =1,000 – 4P and the MC = Q + 20.
Given that TFC is 10% of TR at the revenue maximizing level
(i) Derive the TC (total cost)
First find P
Q/4 =1000/4 – 4P/4
0.25 Q =250-P
P = 250 – 0.25Q
Hence TR = 250 – 0.25Q (Q)
TR = 250 Q- 0.25Q^2
Integrate MC = Q + 20
Q^2/2 + 20Q
TC = 0.5Q^2 + 20 Q
Then we equate:
250Q – 0.25Q^2 = 0.5Q^2 + 20 Q
250q – 20q = 0.5 Q^2 + 0.25Q^2
230Q/Q = 0.75Q^2/Q
230/0.75 = 0.75Q/Q = 307
(ii) What price should the company charge to achieve a profit of $7,320
We know Q = 307
Profit = p(307) – the value you derived from the TC equation
P(307) – 0.5 (307)^2 + 20 (307)
307 P = 47 124.50 + 6140 = 7320
307 P = 53264.50 +7320
307 P/307= 60 584.50/307
P= 197.34 units to...