Answer to Question #199032 in Microeconomics for Sofo

Question

Suppose marginal cost and thus market supply, for an industry is given by the equation P = 4Q S + 20. Also suppose the market demand curve is given by the equation Q D = 40 – 0.5P

i. Determine the equilibrium price and quantity for this industry assuming it is competitive market. 2marks

ii. Assuming government considers the current equilibrium price too high for the market and decides to set the new equilibrium price at 45, describe what the state of the market will look like 2marks CR,4marks

c) The short run production assumes there is at least one fixed factor input. The production function relates the quantity of factor inputs used by a business to the amount of output that result. Using an appropriate diagram explain the short run production and stages of production.

Answer 1

Given

$P=4Q_s+20\\ P-20=4Q_s$

$Q_s=P-\frac{20}{4}$

$Q_d=40-0.5P$

(i) The equilibrium price and quantity is where :

$Q_d=Q_s$

$40-0.5P=P-\frac{20}{4}$

$160-2P=P-20\\3P=180\\P=60$

$Q_d=40-0.5\times 60\\40-30=10$

Equilibrium Price=60 and equilibrium quantity=10

(ii) When the government decides to set the new equilibrium price at 45,this represents a price ceiling.

When the price ceiling P=45 is being set below the equilibrium price being 60,quantity demanded Q_d exceeds the quantity being supplied Q_s and there would be excess demand or shortages.This is being depicted below :

(iii) The short run production and stages of production are :

Stage 1 is being extended with zero input of variable factor to the input level where it had been analyzed that the average product is maximum.The fixed factor under this stage are being excessive.The output could in turn be increased through increase in variable input being relative to a fixed input.

At the beginning of stage 2, the marginal returns in turn start to decrease and the total product is at its maximum.

In Stage 3, the marginal product is being found to be negative and total production declines at the same time. This implies adding more values to the variable inputs in turn seems to be very counterproductive.