Question #47812

Suppose that the market for premium cheese can be characterized by the following equations. QS = â€“6 + (3/2)P QD =14 â€“ (1/2)P
where QS and QD are quantities P is the price.
(a) Graph the supply and demand curves. Calculate and identify on your graph the equilibrium price and
quantity.
(b) Calculate both the demand and supply elasticity around the equilibrium point. [Hint: you can use either the point method or the average arc (midpoint) method.]
(c) Would a small decrease in the number of cheese firms lead to higher or lower spending on cheese? Explain with reference to your answer from part (b).
(d) Suppose the government imposes a per unit tax on producers of 8/3 dollars. What is the new equilibrium price and quantity traded? On a per unit basis, how much of the burden of this tax is borne by consumers? producers? Make sure to show your calculations. [Hint: When adding the tax to the supply curve, make sure you shift it up, not to the right.]

Expert's answer

QS = –6 + (3/2)P, QD =14 – (1/2)P

(a) Equilibrium price and quantity can be found in the point, where Qd = Qs, so:

14 - 0.5P = -6 + 1.5P

2P = 20

Pe = $10

Qe = 14 - 0.5*10 = 9 units.

(b) The demand and supply elasticities around the equilibrium point can be found as the derivatives from the supply and demand curves, that's why Ed = -1/2, Es = 3/2, so demand is inelastic and supply is elastic.

(c) A small decrease in the number of cheese firms lead decrase in quantity supplied and even smaller increase in price, so as the demand is inelastic, spending on cheese will be almost the same.

(d) If the government imposes a per unit tax on producers of 8/3 dollars, the new equilibrium price and quantity traded will be:

-6 + 3/2(P - 8/3) = 14 - 1/2P

2P = 24

Pe2 = 12

Qe2 = 14 - 1/2*12 = 8 units.

The most part of this tax is borne by consumers.

(a) Equilibrium price and quantity can be found in the point, where Qd = Qs, so:

14 - 0.5P = -6 + 1.5P

2P = 20

Pe = $10

Qe = 14 - 0.5*10 = 9 units.

(b) The demand and supply elasticities around the equilibrium point can be found as the derivatives from the supply and demand curves, that's why Ed = -1/2, Es = 3/2, so demand is inelastic and supply is elastic.

(c) A small decrease in the number of cheese firms lead decrase in quantity supplied and even smaller increase in price, so as the demand is inelastic, spending on cheese will be almost the same.

(d) If the government imposes a per unit tax on producers of 8/3 dollars, the new equilibrium price and quantity traded will be:

-6 + 3/2(P - 8/3) = 14 - 1/2P

2P = 24

Pe2 = 12

Qe2 = 14 - 1/2*12 = 8 units.

The most part of this tax is borne by consumers.

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