Question

A vegetable fiber is traded in a competitive world market, and the world price is $9 per pound. Unlimited quantities are available for import into the United States at this price. The U.S. domestic supply and demand for various price levels are shown as follows:

a. What is the equation for demand? What is the equation for supply?

b. At a price of $9, what is the price elasticity of demand? What is it at a    price of $12?

c. What is the price elasticity of supply at $9? At $12?

d. In a free market, what will be the U.S. price and level of fiber imports? 

Answer 1

The equation for demand

i will take two (Q,P) pairs to help me calculate the slope that will be the inverse of the elasticity;

the pairs selected are,

$(34,3), (28,6)$

Find the slope as follows;

$\frac{\Delta P }{\Delta Q} = \frac{ 6-3}{28-34}= -\frac{1}{2}$

To find the demand function we introduce an unknown pair of Q and P

$-\frac{1}{2} = (16,12), (Q,P)$

The equation is therefore;

$P = 28-Q$

The equation for supply

$(6,9), (10,15)$

Find the slope

$\frac{\Delta P }{\Delta Q} = \frac{ 15-6}{10-6}= \frac{3}{2}$

$\frac{3}{2} = (12,18), (Q,P)$

solving this gives the supply equation as;

$P=\frac{3}{2}Q$

c)The price elasticity of demand at $9

$\frac{\Delta Q }{\Delta P}= \frac{22}{9} =2.4$

The price elasticity of demand at $12

$\frac{\Delta Q }{\Delta P}= \frac{16}{12} =1.33$

The price elasticity of supply at $9

$\frac{\Delta Q }{\Delta P}= \frac{6}{9} =0.667$

The price elasticity of supply at $12

$\frac{\Delta Q }{\Delta P}= \frac{8}{12} =0.667$

d) here, we will equate the demand and supply functions obtained above.

 $28-Q =\frac{3}{2}$

$Q= 26.5$

$P = 39.75$