Question

The demand for Fab-4 ice cream is given by p = α − βq . The supply of Fab-4 ice cream is provided by John, Paul, George and Ringo, each of whom faces an identical cost function ci = cqi , i = 1,2,3,4. John and Paul are early risers and produce their ice cream at 7.00am.

George and Ringo wake up a little later and produce their ice cream at 8.00am. The market opens at 9.00am:

1. (a) Calculate the equilibrium total output of Fab-4 ice cream.

2. (b) Calculate the equilibrium outputs and profits for John, Paul, George and Ringo.

Answer 1

demand =  p = α − βq

cost function ci = cqi , i = 1,2,3,4

their are 4 supplier so, perfect competition then price = marginal cost

marginal cost = d(cqi) / dqi = c

price (p) = c

(a) the equilibrium total output of Fab-4 ice cream.

c = α − βq

q =  (α - c) / β answer

(b)the equilibrium outputs and profits for John, Paul, George and Ringo.

as all having same cost function so, will have equal market share

each will produce   (α - c) / 4β answer