At the St. Lawrence Market, the demand for tomato is given by P = 11 - 0.1 Q d ,

Question

At the St. Lawrence Market, the demand for tomato is given by P = 11 - 0.1Qd, where Qd is in thousands of bushels of tomato per week, and P is the price per bushel. The farmers produce tomato according to the supply function P = 0.1Qs, where Qs is in thousands of bushels of tomato per week.

(a) Find the market equilibrium price and quantity of tomato at the St. Lawrence Market.

(b) What is the price elasticity of demand at the market equilibrium.

(c) Suppose that there is an increase in supply due to good weather conditions. What will happen to the total revenue of tomato farmers?

Explanation / Answer

P=11-.1Q    ----------------demand function

P=.1Q ----------------------Supply function

A.

At equilibrium,

Demand = Supply

11-.1Q = .1Q

.2Q=11

Q = 11/.2 = 55

P = .1*55 = 5.5

Thus, equilibrium quantity is 55 (thousands of bushel of tomato per week) and equilibrium price is 5.5 (price per bushel).

B.

P=11-.1Q    ----------------demand function

B.

E = (P/Q)*(dQ/dP) = Price elasticity of demand at equilibrium

dQ/dP = d/dP(11-.1Q) = -.1

E = (5.5/55)*(-.1) = -.01

C.

Due to good weather condition, supply of tomato will increase. Further, supply will take place at reduced prices and it will increase the demand. Up to a certain level of decrease in price, revenue will increase. With further decrease in price, revenue will decrease.

For example

At Price 5.5 (price per bushel),

Revenue = 55*5.5 = 302.5

At price 4.5

Revenue = 65*4.5 = 292.5

Here, demand increases with decrease in price but total revenue also comes down.

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