Answer to Question #277382 in Microeconomics for philo

Question

The market demand functions in a competitive industry is represented by industry, have identical cost function:

C=Q-Q2+0.5Q3 where C is the cost of a firm and q is the quantity produced by each. Calculate;

i) The output produced by each firm in the long run. (5 Marks)

ii) The longrun equilibrium price. (5 Marks)

iii) The equilibrium number of firms. (5 Marks)

iv) Write short notes on indifferences curves. 

Answer 1

Solution:

i.). Demand function: Q(p)=220-p

Inverse demand function: P = 220 – Q

TR = (220 – Q) x Q = 220Q – Q²

MR = $\frac{\partial TR} {\partial Q}$ = 220 – 2Q

TC = Q-Q²+0.5Q³

MC = $\frac{\partial TC} {\partial Q}$ =1 – 2Q + 1.5Q²

Set MR = MC:

220 – 2Q = 1 – 2Q + 1.5Q²

Q = 12

The output produced by each firm in the long run = 12

 

ii.). Long-run equilibrium price:

Substitute in the inverse demand function:

P = 220 – Q = 220 – 12 = 208

Long-run equilibrium price = 208

 

iii.). The equilibrium number of firms = 48/12

=4 firms

 

iv.). An indifference curve refers to a graph showing the combination of two goods that give the consumer equal satisfaction and utility. Each point on an indifference curve indicates that a consumer is indifferent between the two and all points give him the same utility. The shape of an indifference curve is downward-sloping convex to the origin.