3The demand function for a good is Q20010P where Qisthe quan

3)The demand function for a good is Q=200-10P where Qisthe quantity and P is the pnce. Calculate the pnce elast city of demand at prices of $5, $10, and S15 (ie, as the price changes from $5 to $10 and as it changes froen $10 to $15) to show how it changes as you move along this linear demand curve. Is the demand for this item price elastic, price inelastic or unit elastic and what does this mean to be price elastic or price inelastic? (6 points) pe here to search

Solution

Q=200-100P

If P=$5, then Q= 200 – 10(5)= 200-50=150

If P=$10, then Q= 200 – 10(10)= 200-100=100

If P=$15, then Q= 200 – 10(15)= 200-150=50

Price elasticity of demand (PED)= % change in quantity demanded /% change in price of the good.

% change in quantity demanded = ((New quantity-old quantity)/old quantity)) x 100

If price changes from $5 to $10

Old quantity 150     Old price $5

New quantity 100   New price $10

% change in quantity demanded= ((100-150)/150)) x100

                                                         =(-50/150) x100

                                                       = -33.33%

% change in price = ((New price-old price)/old price)) x 100

                                 =((10-5) /5)) x100

                                 = (100) x 100

                                 = 100%

Price elasticity of demand = -33.33/100= -0.33

The sign does not matter, PED is always stated without the sign. It is inelastic since Ped is <1. Price is inelastic if one percent change in price produces less than one percent change in quantity demanded

If price changes from $10 to $15

Price elasticity of demand (PED)= % change in quantity demanded /% change in price of the good.

% change in quantity demanded = ((New quantity-old quantity)/old quantity)) x 100

Old quantity 100     Old price $10

New quantity 50    New price $15

% change in quantity demanded= ((50-100)/100)) x100

                                                         =( -50/100) x100

                                                       = -50%

% change in price = ((New price-old price)/old price)) x 100

                                 =((15-10) /10)) x100

                                 = (5/10) x 100

                                 = 50%

Price elasticity of demand = -50/50= -1

The sign does not matter, PED is always stated without the sign. It is unit elastic since PED is =1. Unit elasticity means if one percentage change in price produces one percent change in quantity demanded.