Suppose that the government imposes a price support (price floor) on processing tomatoes at $65 per ton. The government will buy as much as farmers want to sell at that price. Thus, processing firms pay $65. Use the information in Question 3.6 to determine how many tons of tomatoes firms buy and how many tons the government buys. Illustrate your answer in a supply-and-demand diagram.

Question 3.6

Green et al. (2005) estimated the supply and demand curves for California processing tomatoes, which are used to produce tomato paste. The supply function is ln(Q) = 0.2 + 0.55 ln(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 ln(Q) = 2.6 - 0.2 ln(p) + 0.15 ln(p_t), where p_t is the price of tomato paste 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.