question_answer

                                    Suppose, free entry and exit are allowed in a freely competitive market and there are identical firms in the market. Following are the demand and supply functions of such a market.   Market demand function\[({{q}_{d}})=800-P\] The supply function of a single firm\[({{q}_{s}})\]=10+P   for \[P\ge 20\]             For P<20 Find out the equilibrium price, quantity and number of firms. Or Suppose a freely competitive market has identical firms and free entry and exit are also allowed. Market demand function and the supply function of a single firm are given below. Market demand function\[({{q}_{d}})=590-P\] Market supply function \[({{q}_{d}})=8+5P\] for \[P\ge 10\]and\[=0\]for\[P<10\]

(i) What is the significance of P=10?

(ii) At what price will the market be in equilibrium? State the reason.

(iii) Calculate the equilibrium quantity.

(iv) How many firms are required in the market?

Answer:

From the supply function, we have learnt that the minimum Average Cost (AC) is Rs.20 and no firm would be ready to sell at price below minimum of AC, Hence, in the situation of free entry and exit, equilibrium price will always be equal to minimum AC. Hence, in this situation, equilibrium price will be\[{{P}_{0}}\]=Rs.20 (equal to minimum (AC)                                                                            At this price, market supply will be equal to market demand. From the demand function, we can get the equilibrium quantity by substituting in the function the value of price\[{{q}_{0}}=800-20=\]780 units                                                               At equilibrium price\[({{P}_{0}}=Rs.20)\], each firm supplies\[{{q}_{0p}}=10+20=\]30 units Hence, equilibrium number of firms will be, \[{{N}_{0}}=\frac{{{q}_{0}}}{{{q}_{0p}}}=\frac{780}{30}=\]26 firms Thus, given the market demand function and supply function of a firm when free entry and exit are allowed, Equilibrium price =Rs.20. Equilibrium quantity = 780 units, Total number of firms =26                Or (i) P=10 suggests that in the situation of free entry and exit, equilibrium price can neither be greater nor less than Rs.10. If the market price becomes greater than? 10, Excess supply emerges and price tends to fall till it becomes equal toRs.10. On the other hand, if market price becomes smaller thanRs.10, excess demand emerges and price tends to rise till it reachesRs.10. (ii) From the supply function,\[{{q}_{f}}^{s}\]for P <10, we have learnt that the minimum Average Cost (AC) is Rs.10. In the situation of free entry and exit, equilibrium price is always equal to minimum AC. Hence, in this case, market will be in equilibrium at the price of Rs.10, (iii) From the demand function, we can get the equilibrium quantity by substituting the value of price.             \[{{q}_{0}}=590-P=590-10=580\]units (iv) At equilibrium price\[({{p}_{0}})\]=10, each firm supplies \[{{q}_{0}}_{f}=8+5\times 10=58\] Hence, the number of firms required = \[\frac{580}{58}\]=10 firms