Question

"Consider the perfectly competitive market for smoothies in Anteaterville. The supply of smoothies is given by Q=200 p and demand for smoothies is given by Q=1200-100p, where in each case"

Answer 1

The equilibrium price and quantity in the perfectly competitive market for smoothies in Anteaterville are
`\( P^* = $8 \) and \( Q^* = 600 \)` units, respectively.

Step-by-step explanation:

In a perfectly competitive market, the equilibrium occurs where the quantity demanded equals the quantity supplied. We find this equilibrium by setting the demand and supply equations equal to each other:

`\[ 1200 - 100p = 200p. \]`

Solving for
`\( p \)`, we get
`\( p^* = $8 \)`. Substituting this equilibrium price back into either the demand or supply equation gives us the equilibrium quantity. Using the supply equation
`\( Q = 200p \)`, we find
`\( Q^* = 600 \)`.

This equilibrium price of $8 means that consumers are willing to buy 600 smoothies at this price, and producers are willing to supply the same quantity. At any other price, there would be a shortage or surplus, leading to adjustments in the market.

Perfect competition implies that firms are price takers, meaning they take the market price as given. In this case, the equilibrium price is determined solely by the intersection of the supply and demand curves. The resulting quantity reflects the efficient allocation of resources in the market. The equilibrium quantity of 600 smoothies and the price of $8 represent the point where consumer demand aligns with producer supply, maximizing societal welfare in the Anteaterville smoothie market.