https://file.aiquickdraw.com/mathbot/file/1725908512227ln3g8p1s.jpg

Let's solve the given problems step by step.

### Given:
1. The demand equation for new cars and light trucks is:
   \[
   q = -0.15p + 33 \quad \text{(in million vehicles sold)}
   \]
2. The supply equation for new cars and light trucks is:
   \[
   q = 3.85p - 151 \quad \text{(in million vehicles supplied)}
   \]

#### (a) Finding the equilibrium price:
The equilibrium price occurs when the quantity demanded equals the quantity supplied. Therefore, set the two equations equal to each other:

\[
-0.15p + 33 = 3.85p - 151
\]

Let's solve for $ p $.

#### (b) Estimating the shortage or surplus at $46,300:
- Convert $46,300 to thousand dollars: $ p = 46.3 $
- Calculate the quantity demanded and supplied at this price.
- Find the difference to determine if there is a surplus or shortage.

I'll calculate both parts now.### Solution:

#### (a) The equilibrium price:
The equilibrium price is $ \mathbf{46,000} $ dollars (or $46 thousand).

#### (b) Shortage or surplus at a price of $46,300:
At a price of $46,300, there is an estimated **shortage** of $ \mathbf{1.2} $ million vehicles.

Would you like any further details, or do you have any questions?

### Follow-up Questions:
1. How would a shift in the supply curve affect the equilibrium price?
2. What factors could cause the demand for new cars and light trucks to increase?
3. How would a government subsidy on cars affect the equilibrium?
4. If the supply elasticity increases, what will happen to the surplus or shortage at the same price?
5. How would a recession impact both the demand and supply equations?

### Tip:
In economics, analyzing both price elasticity of demand and supply helps understand how sensitive quantities are to price changes, impacting market equilibrium.

Annual sales of new cars and light trucks in a certain country from 2015–2019 can be approximated by the following when the price (in constant 2021 dollars) was $p thousand: q = -0.15p + 33 million vehicles sold. (a) If car dealers were prepared to supply q = 3.85p - 151 million vehicles at a sale price of $p, what would have been the equilibrium price (in dollars)? (b) The actual average sale price in constant 2021 dollars was $46,300 in 2019. Estimate the projected shortage or surplus (in million of vehicles) at that price.

Explore how to calculate the equilibrium price and estimate shortages or surpluses in car sales using linear equations in economics. Solve for equilibrium by setting demand and supply equal, and estimate shortages at given prices. Suitable for undergraduate students studying economics or math.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation