How to calculate the intersection of two polygons?

Economics questons help?

• Consider a duopoly supplying mineral water. There are two mineral springs and there are two firms supplying mineral water from these two springs. You have to take your own bottle to fill and the firms incur NO cost in production. Their revenue and profit are the same. Firm 1: This firm allows q1 litres to be filled based on the calculation of a profit maximisation exercise. Firm 2: This firm allows q2 litres to be filled, also based on a profit maximisation exercise as above. The market demand function is P = 12- Q, where Q is the total amount of output (total number of litres) supplied by the two firms taken together. REQUIRED: 1. Calculate the price per litre if each firm allows 3 litres to be filled (ie q1 = q2 = 3). 3. Calculate the profit of Firm 1 and Firm 2 if Firm 1 supplies 3 litres (q1 = 3) and Firm 2 supplies 4 litres (q2 = 4) 4. Calculate the profit of each firm if they supply 4 litres each (ie q1 = q2 = 4) 5. Write down the expression for the profit of Firm 1 as a function of q1 and q2 6. Write down the expression for the profit of Firm 2 as a function of q1 and q2 7. Take the partial derivative with respect to q1 of the profit function of Firm 1 and set it equal to zero. Then write q2 as a function of q1 Plot q2 (on the Y-axis) as a function of q1(Xaxis) 8. Take the partial derivative with respect to q2 of the profit function of Firm 2 and set it equal to zero. Then write q2 again as a function of q1. Again plot q2 (on the Y-axis) as a function of q1(X-axis) 9. Solve for q1 and q2 from the two equations in 7 and 8 above using whichever method you wish. 10. Solve for q1 and q2 from the two equations in 7 and 8 above by finding the intersection of the two lines you are asked to draw in 7 and 8 above. Make sure that you get the same answer as in 9. 11. Calculate the price per litre at the above values of output following from the profit maximisation exercises in 7 and 8 above. 12. Now suppose the two firms merge to form a monopoly. What would be profit maximising quantity supplied by this monopoly? 13. What would be the price per litre charged by the monopoly above?

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