1. The function of demand of a company is the following: P= 1200-2Q2 It has the...

1. The function of demand of a company is the following: 
P= 1200-2Q²It has the following functions of fixed and variable costs: 
CF= 2000
CV= Q³-(245/4)Q² +(3057/2)Q
Find: 
a) Quantity and price that maximize the earnings.
b) Value of the profits

Solutions

Expert Solution

P = 1200 - 2Q²

Total cost (TC) = CF + CV = 2,000 + Q³ - 61.25Q² + 1,528.5Q

Marginal cost (MC) = dTC/dQ = 3Q² - 122.5Q + 1,528.5

(a) Earnings (profits) are maximized when Marginal revenue (MR) equals MC.

Total revenue (TR) = P x Q = 1200Q - 2Q³

MR = dTR/dQ = 1200 - 6Q²

1200 - 6Q² = 3Q² - 122.5Q + 1,528.5

9Q² - 122.5Q + 328.5 = 0

Solving this quadratic equation using online solver,

Q = 9.94 or Q = 3.67

(b) Profit = TR - TC = (1200Q - 2Q³) - (2,000 + Q³ - 61.25Q² + 1,528.5Q) = - 328.5Q + 61.25Q² - 3Q³ - 2,000

When Q = 9.94, Profit = -(328.5 x 9.94) + [61.25 x (9.942)²] - [3 x (9.94)³] - 2,000 = -3,265.29 + 6,051.72 - 2,946.32 - 2,000

= - 2,159.89

When Q = 3.67, Profit = -(328.5 x 3.67) + [61.25 x (3.67)²] - [3 x (3.67)³] - 2,000 = - 1,205.60 + 824.97 - 148.29 - 2,000

= - 2,528.92

In both cases profit is negative, so this is a loss-minimizing firm. Loss is minimized (= -2,159.89) when Q = 9.94 units.

Rahul Sunny answered 1 year ago

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