Market Equilibrium: Constant Elasticity of Demand & Supply [Perloff (2014, 3e),

Question

Market Equilibrium: Constant Elasticity of Demand & Supply [Perloff (2014, 3e), Chapter 2, Problem 3.3] Green, Howitt, and Russo (2005) estimate the supply and demand curves for California processing 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 p1, where pt is the price of tomato paste (which is what processing tomatoes are used to produce) in dollars per ton. In 2002, pt = 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 the quantity of processing tomatoes (rounded to two digits after the decimal point). Draw the supply and demand curves (notes that they are not straight lines), and label the equilibrium and axes appropriately.

Explanation / Answer

Answer:-

Qs = 0.2 + 0.55P

Qd = 2.6 - 0.2P + 0.15Pt

In 2002, Pt = 110

Ans:- A. now find demand function for processing tomatoes

Qd = 2.6 - 0.2P + 0.15 * (110)

Qd = 2.6 - 0.2P + 16.5

Qd = 19.1 - 0.2P

Ans:-B   Now find the equilibrium price and the quantity of processing tomatoes

Qd = Qs

19.1 - 0.2P = 0.2 + 0.55P

19.1 - 0.2 = 0.55P + 0.2P

0.75P = 18.9

P = 18.9 / 0.75

P = 25.2

Now Put P value in Qd equation

Qd = 19.1 - 0.2 * (25.2)

Qd = 14.06

Ans: C Diagram

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