The demand equation for a product sold by a competitive firm in UAE is given by the following equation and firms sell their product at 100 AED:
Q = 500 – 10P
The total cost equation of the firm is given by the following equation:
TC = 80 + 20Q + 0.2Q2
a. The inverse demand function views price as a function of Quantity.
Q= 500 - 10P
10P= 500 -Q
P= 50- (1/10) Q
b. TC= 80 +20Q + 0.2Q2
MC= d(TC)/ dQ
MC= 20+ 0.4Q
c. TR= PQ
TR= [50- (1/10) Q]Q
TR= 50Q- (1/10)Q2
MR= d(TR)/dQ
MR= 50- (1/5) Q
d. Profit is maximised at an output level where P= MC
50-(1/10)Q = 20+ 0.4Q
50-0.1Q= 20+ 0.4Q
30= 0.4Q+ 0.1Q
30= 0.5Q
60= Q
e. P= 50- (1/10)Q
P= 50 - (1/10) 60
P= 50 - 6
P= 44
AT Q=60, MC= 44 TOO.
f. PROFIT= TR- TC
PROFIT = 50Q- (1/10)Q2 - (80 +20Q + 0.2Q2)
= 50Q- (1/10)Q2 - 80 -20Q - 0.2Q2
= 30 Q - 0.3Q2 - 80
AT Q = 60 , PROFIT = 30(60) - 0.3( 60)2 -80
= 1800 - 1080 - 80
= 640
g. The total cost function consists of fixed cost and variable cost . Fixed cost exist only in Short run. So the cost function says that the firm is in Short run.
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