Question

suppose, while rummaging through your uncles closet, you found the original painting of dogs playing poker, a valuable piece of art. you decide to set up a display in your uncles garage. the demand curve to see this valuable piece of art is as shown in the diagram below. instructions: on the graph below, use the drop - down menu to indicate whether demand is elastic, inelastic, or unit elastic at each point. graph summary instructions tools reference point at (1, $10) reference point at (3, $6) reference point at (4, $4) legend demand point 1 at (1,10) point 2 at (3, 6) demand for dogs playing poker price (dollars/visit) 0 1 2 3 4 5 6 7 quantity (visitors/day) 14 12 10 8 6 4 2 select select select

Explanation:

Step1: Recall elasticity formula

The price - elasticity of demand formula is $\epsilon=\frac{\%\Delta Q}{\%\Delta P}=\frac{\frac{\Delta Q}{Q_1}}{\frac{\Delta P}{P_1}}=\frac{\Delta Q}{\Delta P}\times\frac{P_1}{Q_1}$.

Step2: Calculate elasticity for point (1, 10)

Let's consider a small change moving down the demand curve. Suppose we move to the next visible point (3, 6). $\Delta Q = 3 - 1=2$, $\Delta P=6 - 10=- 4$, $P_1 = 10$, $Q_1 = 1$. Then $\epsilon=\frac{2}{-4}\times\frac{10}{1}=- 5$. Since $|\epsilon| = 5>1$, demand is elastic at point (1, 10).

Step3: Calculate elasticity for point (3, 6)

Suppose we move from (3, 6) to (4, 4). $\Delta Q=4 - 3 = 1$, $\Delta P=4 - 6=-2$, $P_1 = 6$, $Q_1 = 3$. Then $\epsilon=\frac{1}{-2}\times\frac{6}{3}=-1$. Since $|\epsilon| = 1$, demand is unit - elastic at point (3, 6).

Step4: Calculate elasticity for point (4, 4)

Suppose we move from (4, 4) to a point further down the curve. Let's assume the next point is such that if we consider a small movement, say to a point where $Q$ increases by 1 and $P$ decreases by 2. $\Delta Q = 1$, $\Delta P=-2$, $P_1 = 4$, $Q_1 = 4$. Then $\epsilon=\frac{1}{-2}\times\frac{4}{4}=-\frac{1}{2}$. Since $|\epsilon|=\frac{1}{2}<1$, demand is inelastic at point (4, 4).

Answer:

At point (1, $10$): Elastic
At point (3, $6$): Unit - elastic
At point (4, $4$): Inelastic