A competitive firm uses two variable factors to produce its output, with a production function q = min{x1, x2}.The price of factor 1 is $8 and the price of factor 2 is $5. Due to a lack of warehouse space, the company cannot use more than 10 units of x1. The firm must pay a fixed cost of $80 if it produces any positive amount but doesn't have to pay this cost if it produces no output. What is the smallest integer price that would make a firm willing to produce a positive amount?

Question

Quizplus · Accepted Answer

To produce a positive amount, the firm must cover both variable and fixed costs. The cost of producing q units is 8q + 5q + 80 = 13q + 80. To break even, the price must be at least 13 + 80/q. For the smallest integer price, assume q = 10 (since x1 is limited to 10), then the price must be at least (13*10 + 80)/10 = 21.

A Competitive Firm Uses Two Variable Factors to Produce Its