Answer to Question #195072 in Macroeconomics for simegnew

Question

Assume a firm engaging in selling its product and promotional activities in monopolistic

competition face short run demand and cost functions as Q = 20-0.5P and TC= 4Q2

-8Q+15,

respectively. Having this information (5 marks)

a) Determine the optimal level of output and price in the short run.

b) Calculate the economic profit (loss) the firm will obtain (incur).

c) Show the economic profit (loss) of the firm in a graphic representation

Answer 1

a)The optimal volume of output is determined from the condition of profit maximization in the market of imperfect competition:

MC = MR

We find the marginal cost as a derivative of the total cost:

$MC = (TC)’ = (4Q^2-8Q+15)’ = 8Q-8$

$Q = 20-0.5P$

$P=\frac{20-Q}{0.5}=40-\frac{Q}{2}$

Calculate the total revenue function:

$TR = P\times Q = (40-\frac{Q}{2}) \times Q = 40Q – \frac{Q^2}{2}$

We differentiate this function and define the marginal revenue function:

$MR = (TR)’ = (40Q – \frac{Q^2}{2})’ = 40 – Q.$

Так как MC = MR, то

8Q-8 = 140– Q

Q=14.67 optimal output volume.

Next, we find the optimal price:

$P = 40-\frac{Q}{2} =40-\frac{14.67}{2}=32.665$

b)

he profit of a monopolistically competitive firm is found by the formula:

$P = TR – TC = P × Q – TC =(32.665× 14.67) –((14.62)^2-8\times14.67 + 15)= 467.201$

c)