Question

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 +
0.2Q ^{2}**

- Derive the inverse demand function.
**(1 Point)**

- What is the firm’s MC function?
**(1/2 Point)**

- What is the firm’s MR function?
**(1/2 Point)**

- What is the firm’s profit maximizing level of output?
**(1 Point)**

- What is the firm’s profit maximizing level of price?
**(1/2 Point)**

- How much profit will the firm make?
**(1 Point)**

- Is the firm in the short run or long run?
**(1/2 Point)**

Answer #1

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 + 0.2Q^{2}

MC= d(TC)/ dQ

MC= 20+ 0.4Q

c. TR= PQ

TR= [50- (1/10) Q]Q

TR= 50Q- (1/10)Q^{2}

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)Q^{2} - (80 +20Q +
0.2Q^{2})

= 50Q- (1/10)Q^{2} - 80 -20Q - 0.2Q^{2}

^{=} 30 Q - 0.3Q^{2} - 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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