uninformed consumers whose numbers being relatively few results in making it unprofitable to 3. Let the demand for products I and 2 be q,=10-2p,+p, and 2=10+P,-2p2, where q the quantity of good i and Pi is the price of good i. Assume production costs are zero. Calculate the prices that two separate monopolies would charge when each regards the other's price as eyond its control. Calculate the prices that a single monopoly of both goods will charge. Which rrangement would the consumers prefer (you have to show it, not only argue). Using the measure of product differentiation that we have discussed in class, obtain a measure of product differentiation for the set of demand functions given here.( Remember you have to first obtain the demands in the inverse form Firm I's maximization problem is max Il P,(10-2p,+ p2) Best response of the firm is given as an, / ap.=0 10-4p1+P2=0 10+P2 PI 4 By symmetry the best response of the firm 2 is given as 10+P1 P Plugging(2)into(1)we get p, =10/3 and p2=10/3 If there is a single monopoly then he would maximize the joint profit ∏=∏1+∏12=P1(10-2p1+p2)+P2(10-2p2+P1) First order condition for the choice of the price 1 anl/ 0 →10-4p1+P2+P2=0 First order condition for the choice of the price 2 a/p2=0 →10-4p2+P1+P1=0 We can use equations 3 and 4 to solve for two pricesuninformed consumers whose numbers being relatively few results in making it unprofitable to deviate. 3. Let the demand for products 1 and 2 be 1 21 = − 210 + ppq and 2 21 = + − 210 ppq , where qi is the quantity of good i and pi is the price of good i . Assume production costs are zero. Calculate the prices that two separate monopolies would charge when each regards the other’s price as beyond its control. Calculate the prices that a single monopoly of both goods will charge. Which arrangement would the consumers prefer (you have to show it, not only argue). Using the measure of product differentiation that we have discussed in class, obtain a measure of product differentiation for the set of demand functions given here. (Remember you have to first obtain the demands in the inverse form) Firm 1’s maximization problem is max )210( Π = 11 − + ppp 21 Best response of the firm is given as: 4 10 410 0 0/ 2 1 21 11 p p pp p + = =+−⇒ =∂Π∂ (1) By symmetry the best response of the firm 2 is given as: 4 10 1 2 p p + = (2) Plugging (2) into (1) we get 3/10 * p1 = and 3/10 * p2 = If there is a single monopoly then he would maximize the joint profit )210()210(121 221 12 ++−=Π+Π=Π − + pppppp First order condition for the choice of the price 1 0/ p1 =∂Π∂ 410 0 ppp 221 =++−⇒ (3) First order condition for the choice of the price 2 0/ p2 =∂Π∂ 410 0 ppp 112 =++−⇒ (4) We can use equations 3 and 4 to solve for two prices