Question

you are naighty pine number sell fence panels in a competitive market right now you selling price &130 for a fence panel and you sell 8 panels a day. you are considering changing your price you estimate that if younraise your price to $152 a panel you would sell 7 panels a day. on the othet hand, if you lower your price to $108 a panel you will sell 13 panel a day

Answer 1

The complete question is

You own Naughty Pine lumber and sell fence panels in a competitive market. Right now, your selling price is $130 for a fence panel, and you sell 8 panels a day. You are considering changing your price. You estimate that if you raise your price to $152 a panel, you would sell 7 panels a day. On the other hand, if you lower your price to $108 a panel, you would sell 12 panels a day.

(a) Draw a graph of the above information. Label your axes, and the curve. Be sure your work is clear.

(b) Use the MIDPOINT FORMULA to calculate Ed over the ranges below. Use TWO decimals in your answers.

(i)Calculate the price elasticity of demand for a price change from $130 to $152 and daily Total Revenue if you change your price to $152 a panel 

(ii)Calculate the price elasticity of demand for a price change from $130 to $108 and daily Total Revenue if you change your price to $108 a panel

(c) Should you keep your current price, or raise the price, or lower the price?

Solution

a.

b.

(i)

Mid Point Elasticity formula is given as below.

$E_d =\frac{ (Q_2-Q_1)}{(Q1+Q2)}\times \frac{(P1+P2)}{(P2 -P1)}$

When P₁ = $130, Q₁ = 8 panels

When P₂ = $152, Q₂ = 7 panels

$Ed = \frac{(7-8)}{15}\times\frac{(130+152)}{(152-130)} =\frac{282}{15}\times\frac{1}{-22}=\frac{-282}{330}=-0.8545$

Original daily total revenue$= P_1 Q_1 = 130\times8 =\$ 1040$

New daily total revenue $= P_2 Q_2 = 152\times7 = \$ 1064$

In a case, when Price elasticity of demand is less than one, which represents it is inelastic; therefore, Price increase

Mid Point Elasticity formula is given as below.

(ii)

$E_d =\frac{ (Q_2-Q_1)}{(Q_1+Q_2)}\times\frac{(P_1+P_2)}{(P_2 -P_1)}$

When P₁ = $130, Q₁ = 8 panels

When P₂ = $108, Q₂ = 12 panels

$E_d = \frac{(12-8)}{20}\times\frac{(130+108)}{(108-130) }$

$=\frac{952}{20}\times \frac{1}{-22} = \frac{-952}{440 }= -2.1636$

Original daily total revenue $= P_1 Q_1 = 130\times 8 = \$ 1040$

New daily total revenue $= P_2 Q_2 = 108*12 = \$ 1296.$

(c)

Market being competitive and we see demand to be elastic when we decrease the price. Price should be decreased to gain higher additional revenue.