Question

1. Suppose there is a perfectly competitive industry in Dubai, where all the firms are identical. The market demand for this product is given by the equation: (Kindly answer clearly)

P = 1000 – 2Q

Also, the market supply equation is given by the following equation:

P = 100 + Q.

Furthermore, suppose that a representative firm’s total cost is given by the equation:

TC = 100 + q2 + q

1. What is the equilibrium quantity and price in this market given this information?

2. Calculate the MC function?

3. Calculate the MR function?

4. Calculate the profit maximizing level of output for the firm?

5. Calculate the size of the profit? Show it graphically

6. Is this industry SR or LR?

Answer 1

a) At equilibrium, demand = supply

1,000 - 2Q = 100 + Q

900 = 3Q

Q = 300

At Q = 300, P = 400

b) MC is first derivative of TC with respect to Q = 2Q + 1

c) P = 1,000 - 2Q

Total Revenue = P * Q = 1,000Q - 2Q2

Marginal Revenue is first derivative of total revenue with respect to Q = 1,000 - 4Q

d) Profit maximizing level of output occurs when MR = MC

1,000 - 4Q = 2Q + 1

999 = 6Q

Q = 166.5

e) Profit = Total Revenue - Total cost

Profit = 1,000 * 166.5 - 2 * 166.52 - 100 - 166.52 - 166.5 = 83,066.75

f) This industry in short run because in long run perfectly competitive market earns normal profit when due to entrance of new firms in the market after observing the short run profit of firms.