The following is the description of a cost: total fixed costs are $50 000 per month and the variable cost per unit is $10 when production is under 1000 units. The variable cost drops to $9 per unit after the first 1000 units are produced.

Required

(a) Write the algebraic expression of the cost function and graph it.

(b) Assume that the cost function just described is a reasonable representation of total costs. If the accountant performed regression analysis on weekly observations of this cost and did not realise that there were two relevant ranges, what problems would arise in the cost function that was produced? In other words, how would the cost function be mismeasured?