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 $4 and the price of factor 2 is $1.Due to a lack of warehouse space, the company cannot use more than 15 units of x1.The firm must pay a fixed cost of $90 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?
A)$15
B)$21
C)$5
D)$24
E)$11

Question

Quizplus · Accepted Answer

To determine the smallest integer price that would make the firm willing to produce a positive amount, we need to consider the costs involved in production, including variable and fixed costs. The fixed cost is $90, which the firm must pay if it decides to produce any positive amount. The variable costs depend on the prices of the factors and the quantities used, but without specific details on the production function or how the factors are combined, we can't calculate the exact variable cost. However, we know that the firm will want to cover both its variable and fixed costs to make a profit or at least break even.Given that the firm is competitive, it will take the market price as given and produce where marginal cost equals marginal revenue (price). The smallest integer price that would make the firm willing to produce must at least cover the average total cost (which includes both variable and fixed costs) at the optimal level of production. Without specific details on the production function, we can't calculate this precisely, but we know the firm needs to cover the fixed cost of $90 plus any variable costs.Since we can't determine the exact variable costs from the information provided, we focus on the fixed cost. The firm would need a price that, when multiplied by the quantity produced, exceeds the fixed cost of $90 plus variable costs. The exact price would depend on the quantity produced and the efficiency of the production process (which we can't determine from the given information). However, the question asks for the smallest integer price that makes production viable, implying a price that just covers all costs.Without detailed calculations possible, we infer that the correct answer must be based on the understanding that the firm needs to cover its fixed and variable costs. Among the options given, $11 (E) is a plausible choice for the smallest integer price that could potentially cover costs and make the firm willing to produce a positive amount, assuming very efficient production and low variable costs. This is a theoretical answer based on the information provided and the nature of the question, which seems to require an understanding of the principles of production costs and pricing in a competitive market rather than precise calculations.

A Competitive Firm Uses Two Variable Factors to Produce Its