let one week’s supply and demand functions for gasoline be given by p = d(q)=294 - \\frac{2}{3}q and p =…

let one week’s supply and demand functions for gasoline be given by p = d(q)=294 - \\frac{2}{3}q and p = s(q)=\\frac{5}{3}q, where p is the price in dollars and q is the number of 42 - gallon barrels. (a) graph these equations on the same axes. (b) find the equilibrium quantity. (c) find the equilibrium price.\n(a) choose the graph of d(q) and s(q).\na.\nb.\nc.\nd.\n(b) the equilibrium quantity is \n(c) the equilibrium price is $

let one week’s supply and demand functions for gasoline be given by p = d(q)=294 - \\frac{2}{3}q and p = s(q)=\\frac{5}{3}q, where p is the price in dollars and q is the number of 42 - gallon barrels. (a) graph these equations on the same axes. (b) find the equilibrium quantity. (c) find the equilibrium price.\n(a) choose the graph of d(q) and s(q).\na.\nb.\nc.\nd.\n(b) the equilibrium quantity is \n(c) the equilibrium price is $

Answer

Explanation:

Step1: Recall equilibrium condition

At equilibrium, $D(q)=S(q)$. So we set $294 - \frac{2}{3}q=\frac{5}{3}q$.

Step2: Solve for equilibrium quantity $q$

Add $\frac{2}{3}q$ to both sides of the equation: $294=\frac{5}{3}q+\frac{2}{3}q$. Combining like - terms, we get $294 = \frac{5 + 2}{3}q=\frac{7}{3}q$. Multiply both sides by $\frac{3}{7}$ to solve for $q$: $q = 294\times\frac{3}{7}=126$ barrels.

Step3: Solve for equilibrium price $p$

Substitute $q = 126$ into either the supply or demand function. Let's use the supply function $p=S(q)=\frac{5}{3}q$. $p=\frac{5}{3}\times126 = 210$ dollars.

For part (a), the demand function $p = D(q)=294-\frac{2}{3}q$ is a linear function with a negative slope ($m=-\frac{2}{3}$) and $y$-intercept of 294. The supply function $p = S(q)=\frac{5}{3}q$ is a linear function with a positive slope ($m = \frac{5}{3}$) and $y$-intercept of 0. The correct graph is the one where the two lines intersect at the point $(126,210)$.

Answer:

(a) The graph where the demand line (negative - slope) and supply line (positive - slope) intersect at $(126,210)$ (you need to visually inspect the options to pick the correct one). (b) 126 barrels (c) $210$