I drew a sketch that would provide some guidance and, to tell the truth, I actually drew two sketches: one with the total market demand (two segments here) and the other with the total market supply (a single linear line). I then did a bit of a experiment”: I know “thought that the point (100, 50) is the point on the demand curve and I thought, “kink” “hmmm, what would be the price associated with a quantity supplied of 100 units?” From my graph of the market supply curve, I knew that a quantity of 100 units would result in a price of $25. Since $25 is less than $50 this told me that I should use the market demand curve P = 75 (1/4)Q and the market supply curve to find the equilibrium in the peanut market. So, – 75 (1/4)Q = (1/4)Q – 75 = (1/2)Q Q = 150 units of peanuts Then, using either the market demand curve or the market supply curve you can find the equilibrium price: P = 75 (1/4)Q = 75 (1/4)(150) = $37.50 per unit of peanuts – – P = (1/4)Q = (1/4)(150) = $37.50 per unit of peanuts North East Quantity of Peanuts Q = P Q = P Q = (2)P Produced by each Q = 37.5 of Q = 37.5 units of Q = (2)(37.5) = 75 Country peanuts peanuts units of peanuts Quantity of Peanuts P = 50 - Q P = 100 (1/2)Q P = 50 - Q – Demanded by each 37.5 = 50 - Q 37.5 = 100 (1/2)Q 37.5 = 50 - Q – Country Q = 12.5 units of 125 = units of Q = 12.5 units of peanuts peanuts peanuts Quantity of Peanuts 25 units of peanuts 0 units of peanuts 62.5 units of peanuts Exported by each Country Quantity of Peanuts 0 units of peanuts 87.5 of peanuts 0 units of peanuts Imported by each Country
I drew a sketch that would provide some guidance and, to tell the truth, I actually drew two sketches: one with the total market demand (two segments here) and the other with the total market supply (a single linear line). I then did a bit of a “thought experiment”: I know that the point (100, 50) is the “kink” point on the demand curve and I thought, “hmmm, what would be the price associated with a quantity supplied of 100 units?” From my graph of the market supply curve, I knew that a quantity of 100 units would result in a price of $25. Since $25 is less than $50 this told me that I should use the market demand curve P = 75 – (1/4)Q and the market supply curve to find the equilibrium in the peanut market. So, 75 – (1/4)Q = (1/4)Q 75 = (1/2)Q Q = 150 units of peanuts Then, using either the market demand curve or the market supply curve you can find the equilibrium price: P = 75 – (1/4)Q = 75 – (1/4)(150) = $37.50 per unit of peanuts P = (1/4)Q = (1/4)(150) = $37.50 per unit of peanuts North East Quantity of Peanuts Produced by each Country Q = P Q = 37.5 of peanuts Q = P Q = 37.5 units of peanuts Q = (2)P Q = (2)(37.5) = 75 units of peanuts Quantity of Peanuts Demanded by each Country P = 50 - Q 37.5 = 50 - Q Q = 12.5 units of peanuts P = 100 – (1/2)Q 37.5 = 100 – (1/2)Q 125 = units of peanuts P = 50 - Q 37.5 = 50 - Q Q = 12.5 units of peanuts Quantity of Peanuts Exported by each Country 25 units of peanuts 0 units of peanuts 62.5 units of peanuts Quantity of Peanuts Imported by each Country 0 units of peanuts 87.5 of peanuts 0 units of peanuts