Answer to Question #198930 in Microeconomics for robel legese

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 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) Given:$Q = 20 - 0.5P$

$0.5P = 20 - Q$

$P = 40 - 2Q$ and $TC = 4Q^{2} - 8Q + 15$

Total Revenue = Price × quantity

Profit (π) = Total Revenue - Total Cos

$= (40 - 2Q)Q - (4Q^{2} - 8Q + 15)$

$= 40Q - 20Q^{2} - 4Q^{2} + 8Q -15$

$= 48Q - 6Q^{2} - 15$

π (first order differentiation) $= 48 - 12Q$

$48 = 12 Q$

$Q = 4$

$P = 40 - 2Q$

$= 40 - 2(4)$

$= 40 - 8$

$= 32$

Thus, Quantity is 4 and Price is $32

b) Profit = Total Revenue - Total Cost

$= 48Q - 6Q^{2} - 15$

$= 48(4) - 6(4)^{2} - 15$

$= 192 - 96 - 15$

$= 80$

Thus the economic profit the firm will obtain is $80

c)The diagram shows the profit of the firm.