Question

 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

Determining the optimal output and price in the Short Run

Make P the subject of the demand function;

$Q=20-0.5P$

$Q-20=-0.5P$

$P=20-Q$

The function of profit is;

$Profit =PQ-C$

$(20-Q)Q-4Q^2-8Q+15$

$Profit =12Q-5Q^2+15$

The optimal level of output occurs when the derivative of profit is 0

Therefore;

$\frac{\Delta Profit}{\Delta Q}=12-10Q$ ........(I)

Equating equation i to zero; we obtain

$Q=1.2 units$

We use the value of Q obtained above to calculate the optimal price.

$P= 20-Q$

$P= 20-1.2 = 18.8$

Calculating Profit (Loss)

The profit function

$Profit=12Q−5Q 2 +15$

With value of Q known;

$Profit = 12(1.2) -5(1.44)+15$

$Profit = 22.2$

The graphical representation of the profit is as shown below.