Problem

Green et al. (2005) estimate the supply and demand curves for California processed tomatoes. The supply function is In(Q) = 0.2 + 0.55 In(p), where Q is the quantity of processing tomatoes in millions of tons per year and p is the price in dollars per ton. The demand function is In(Q) = 2.6 - 0.2 In(p) + 0.15 In(p_t) where (p_t) is the price of tomato paste (which is what processing tomatoes are used to produce) in dollars per ton. In 2002, p_t = 110. What is the demand function for processing tomatoes, where the quantity is solely a function of the price of processing tomatoes? Solve for the equilibrium price and quantity of processing tomatoes (explain your calculations, and round to two digits after the decimal point). Draw the supply and demand curves (note that they are not straight lines), and label the equilibrium and axes appropriately.