Predicting Changes in Equilibrium Price and Quantity

Suppose that the market demand for farmed salmon is Q^d = 12 p and the market supply of farmed salmon is Q^s = 9.6 + 0.5p 0.2p_t, where Q is the quantity of salmon in millions of tons per year, p is the price of salmon in dollars per pound, and p_t is the price of tilapia in dollars per pound. The supply function demonstrates that the facilities that are used to farm salmon are also suitable for farming tilapia.

a) Use a market diagram to demonstrate that the equilibrium price and quantity of salmon is implicitly a function of the price of tilapia. That is, show how a change in the price of tilapia will impact the market for farmed salmon. (No need to use numbers here, just sketch and explain.)

b) Using the supply and demand functions, derive the relationship between the price of tilapia and the equilibrium price and quantity of salmon. You should ultimately calculate and . Check your work by calculating the impact of an increase in the price of tilapia from $3 to $6 per pound on the equilibrium price and quantity of salmon.

c) Assuming that the price of tilapia is $3 per pound, calculate the price elasticity of demand for farmed salmon and the price elasticity of supply for farmed salmon. Interpret your findings.

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