Question

Demand for alcohol has been present for much of human history, but supply has faced many forms of restriction for a variety of reasons. Consider a competitive market for wine, where the costs of a typical supplier can be represented by the function c(y)=175+7y2, where y represents bottles of wine produced.

What is the long-run equilibrium price per bottle of wine?

Answer 1

To find the long-run equilibrium price per bottle of wine, one needs to calculate the long-run average cost, find the quantity that minimizes this cost, and then use the original cost function or the LRAC at this quantity to find the price.

Step-by-step explanation:

The student asks about finding the long-run equilibrium price per bottle of wine in a competitive market, given the cost function c(y) = 175 + 7y2, where y represents bottles of wine produced. In the long-run equilibrium of a competitive market, firms will produce at the minimum point of their long-run average cost (LRAC) curve, since this is where they can sell their product at a price that matches the lowest cost per unit and still break even. To determine this price, we first need to find the LRAC function. Calculating the LRAC involves dividing the total cost by the quantity produced. The LRAC function is c(y)/y, which is (175/y) + 7y. To find the bottom of this curve, we take the derivative and set it equal to zero to find the minimizing quantity y. Then, we can use this quantity to calculate the long-run equilibrium price using the original cost function or the LRAC function as they will be equal at that quantity.