The West Chester corporation believes that the demand curve for its product is:
P= 28 - 0.14Q
Where P is price (in $) and Q is output (in units). The firm’s board of directors after a lengthy meeting concludes that the firm should attempt at least for a while to increase its total revenue even if this means lower profit.
a. Why must a firm adopt such a policy?
b. What is the quantity and price should the firm set if it wants to maximise its total revenue?
c. What is the quantity and price equilibrium if the firm’s marginal cost is $14?
a. A firm may adopt the strategy of increasing total revenue even if it means lower profit in order to gain market share, attract more customers, or create brand loyalty. By offering a lower price, the firm can potentially increase the quantity demanded for its product, resulting in higher total revenue despite lower profit margins per unit.
b. To maximize total revenue, the firm should set the quantity at which marginal revenue equals zero. This occurs when the derivative of the total revenue equation with respect to quantity (TR'Q) is equal to zero. In this case, the demand curve is given by P = 28 - 0.14Q.
To find the quantity and price that maximizes total revenue, we need to find the quantity at which marginal revenue (MR) equals zero. In this case, MR is the derivative of the total revenue equation with respect to quantity (TR'Q).
TR'Q = 28 - 0.14Q
MR = TR'Q = 0
0 = 28 - 0.14Q
0.14Q = 28
Q = 28 / 0.14
Q = 200 units
To find the price, we substitute the quantity (Q) into the demand equation:
P = 28 - 0.14Q
P = 28 - 0.14(200)
P = 28 - 28
P = $0
Therefore, to maximize total revenue, the firm should set the quantity at 200 units and the price at $0.
c. To find the quantity and price equilibrium if the firm's marginal cost is $14, we need to find the quantity at which marginal cost equals marginal revenue. This occurs when the derivative of the cost equation with respect to quantity (C'Q) is equal to the derivative of the revenue equation with respect to quantity (R'Q).
Given that the marginal cost is $14 and the demand curve is P = 28 - 0.14Q, we can set up the equation:
MC = MR
14 = 28 - 0.14Q
0.14Q = 28 - 14
0.14Q = 14
Q = 14 / 0.14
Q = 100 units
To find the price, we substitute the quantity (Q) into the demand equation:
P = 28 - 0.14Q
P = 28 - 0.14(100)
P = 28 - 14
P = $14
Therefore, the quantity and price equilibrium, given a marginal cost of $14, is 100 units and $14, respectively.