Question

Suppose the daily demand for soda is given by P = 4 – (2/3)Q and the daily supply of soda is given by P = 1 + (1/3)Q, where P is the dollar price of a can of soda and Q is the number of cans of soda (in thousands).a. Sketch the demand curve and the supply curve.Instructions: Use the tools provided to draw the demand and supply curves. Plot each end point (4 points total).b. How many cans of soda are bought and sold each day? What is the equilibrium price of soda?i. Equilibrium quantity: ____ cansii. Equilibrium price: $ ____ per canc. What is the price elasticity of demand for soda at the equilibrium price?d. What is the price elasticity of supply for soda at the equilibrium price?e. If the price of one of the inputs used to make soda increases, then what will happen to consumers' total expenditure on soda?i. It will decrease.ii. it will remain unchangediii. It will increase.

Answer 1

Answer:

Qe 2

Pe 2

Demand price elasticity -0.60

Supplu price elasticity 3

i. It will decrease

As the demand as a more than proportionate price elasticity will overreact to the input price and their subsequent price increase with a reduce in consumption.

Explanation:

We equalize both to get the equilibrium quantity (Qe)

4 - 2/3Qe = 1 + 1/3Qe

Qe(2/3 + 1/3)  = 4 - 1

Qe = 3

Then we solve for equilibrium price (Pe)

Pe =  4 - 2/3 x 3 = 4 - 2 = 2

Pe = 1 + 1/3 x 3 = 1 + 1 = 2

Price elasticity of demand at equilibrium:

variation in quantity / variation in price

we solve for Q when P = 3 and compare the variation

(1.33-3) / (3 - 2) = -1.66/1  = -1.66

Price elasticity of supply at equilibrium:  ( 6 - 3) / (3 - 2) = 3 / 1 = 3