A firm is pondering the introduction of a new good with a profit contribution of $70 per unit. Each unit of the good uses 2 units of input A and 3 units of input B. The shadow price of A is $10, and the shadow price of input B is $15. Which of the following statements is true?
A) The firm should produce the new good.
B) The opportunity cost of producing the new good is $75.
C) The firm should not produce the new good.
D) Producing the new good will earn a profit of $10.
E) Producing the new good will earn a loss of $5.

Question

Quizplus · Accepted Answer

The shadow prices represent the opportunity cost of using one more unit of each input. Since the shadow price of input A is $10 and one unit of the new good uses 2 units of input A, the opportunity cost of using 2 units of input A is $20. Similarly, the opportunity cost of using 3 units of input B is $45. Therefore, the total opportunity cost of producing one unit of the new good is $65 ($20+$45), leaving a profit contribution of $70. Thus, producing the new good would be profitable and the firm should introduce it. Option A states this, so it is the correct answer. Option B is incorrect because it calculates the total opportunity cost incorrectly by multiplying the shadow prices by the amounts of inputs used, rather than by the amounts of inputs given in the problem. Option C is incorrect because it does not take into account the profit contribution of the new good. Option D is incorrect because it only states the value of the shadow price of input A, which is not relevant to calculating the profit earned by producing the new good. Option E is incorrect because it assumes that the total cost of producing one unit of the new good is $75, which is incorrect.

A Firm Is Pondering the Introduction of a New Good