Answer to Question #194605 in Macroeconomics for etsub

Question #194605

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


1
Expert's answer
2021-05-18T12:30:55-0400

The demand function is given by"Q = 20 \u2212 0.5P\\space \n\n or\\space P = 40 \u2212 2Q"

and the cost function is given by"TC = 4Q^2 \u2212 8Q +\u200915"

Since, in monopolistic competition, equilibrium takes place where Marginal Revenue (MR) = Marginal Cost (MC),

we find MR and MC and equate them. to find our equilibrium P and Q.

By definition, 

"MR=\\frac{d}{dQ}(Total\\space Revenue)"


"=\\frac{d}{dQ}(P\\times Q)"


"=\\frac{d}{dQ}(Q\\times(40-2Q)"


"=\\frac{d}{dQ}(40Q-2Q^2)"


"=40-4Q"


and,

"MC=\\frac{d}{dQ}(Total\\space Cost)"


"=\\frac{d}{dQ}(TC)"


"=\\frac{d}{dQ}(4Q^2-8Q+15)"


"=8Q-8"


Equating MC and MR we get, 


"MC= MR\\\\8Q-8 =40 \u2212 4Q \\\\12Q=48\\\\Q=4"


(a) Hence, number of quantities produced (Q) = 4.


Therefore, the price (P)  = 40 − 2Q = 40 − (2 × 4) = 40 − 8 = 32

per unit. 



(b)

Now, the profit function of the firm, can be written as, 

"\\pi(Q)=Total\\space Revenue-Total\\space Cost\\\\=(P\\times Q)-(TC\\times Q)"

If the above expression is calculated for a numerical value, the following is obtained. 


"\\pi(4)=(32\\times4)-[(4\\times4^2)-8(4)+15]\\\\=128-[64-32+15]\\\\=128-47\\\\=81"


  The economic profit is calculated to be 81 units.



(c)

The economic profit can be shown diagrammatically as the following,




Pc is the competitive price and Pmc is the price under monopolistic competition. Qmc is the equilibrium output.

The grey shaded area is the total amount of profit. 


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS