Question

Kelly sells orange juice in a competitive market on a busy street corner in New York. Her production function is ?(?1, ?2) = ?1 1/3 ?2 1/3, where output is measured in gallons, ?1 is number of pounds of oranges she uses, and ?2 is the number of labor-hours spent squeezing them. ?1 = $16 is the cost of a pound of oranges and ?2 = $2 is the wage rate for orange-squeezers.

At the cost minimizing input bundle, how much labor-hours are spent per pound of oranges? That is,

compute the ratio of x2/x1 at the cost minimizing input bundle

b) What is the optimal inputs bundle to produce 8 units of output in the cheapest way?

c) What is the minimized cost of producing 8 units of output?

d) Calculate the average cost when total cost of production is minimized and output is 8 units

e) If market price of orange juice is $20 per unit (p=$20), conditional on Kelly is now producing 8 units of

output in the cheapest way, what is Kelly’s total profit? Determine Kelly’s supply decision in long run

Answer 1

In the long run either they have to increase production with lowest cost or shut down due to loss injured. At 8 unit it is though cost minimised bundle of inputs but with given price it is not profitable. Hence require producing higher output that increase economies of scale. Sice market is competitive so it is only a price taker.