hello , i have some questions about the above exercise. I am sending you the pronunciation of the exercise and it's answer and i will write here what i have not understood from the solution. 1) in the first sub- question how can we find the q is 16 and how we can find the price is 36 and profits is 512 ( please explain step by step ) 2) in the second sub question how find q is 12 and cartel will produce 24 point and how find profits is 576 3) in the third sub quotation how we find 18 and 30 ?

i have written next to the solutions the points that i want further explanation for how the specific results comes out !

(LCC) if a ea company doe does not agreement for a period then it will & produce the quantity resultion function if we replace the quantity produced by its competion is partnership (12 units). So the quantity that this will produce business will be 18 units. As profits of this business will be is = [100-2 (30)] *18-4-18=46648 how find 18 ? and how hind 30? We know that of the partnership is the relationship that determines the viability 7.-7 So in order for the par - partnership to be viable the M than 576-512 interest rate should is less 6.889. So if the interest rate is 5% 648-576 partnership is sustainable (LCC) if a ea company doe does not agreement for a period then it will & produce the quantity resultion function if we replace the quantity produced by its competion is partnership (12 units). So the quantity that this will produce business will be 18 units. As profits of this business will be is = [100-2 (30)] *18-4-18=46648 how find 18 ? and how hind 30? We know that of the partnership is the relationship that determines the viability 7.-7 So in order for the par - partnership to be viable the M than 576-512 interest rate should is less 6.889. So if the interest rate is 5% 648-576 partnership is sustainable (LCC) if a ea company doe does not agreement for a period then it will & produce the quantity resultion function if we replace the quantity produced by its competion is partnership (12 units). So the quantity that this will produce business will be 18 units. As profits of this business will be is = [100-2 (30)] *18-4-18=46648 how find 18 ? and how hind 30? We know that of the partnership is the relationship that determines the viability 7.-7 So in order for the par - partnership to be viable the M than 576-512 interest rate should is less 6.889. So if the interest rate is 5% 648-576 partnership is sustainable Answer 7 () Each T decides on the quantity it will produce independent of its competitor to maximize its profits. The problem of moximizing 1-11 company 6 the profits of 1-01- I will be: company 0a Max = [100-29 +9) 39-49 From the first order condition an avn AVTI we derive the reaction function 99, of company is = 24-92 2 " The problem of maximizing Max 1 = [100-2(9 +92)]92-492 the profits of 2 will be company Av we derive the reaction function of 2 is KEF company 92 = 24-9 2 70 Solving the follows that the equilliprium quantity Cournot that will produce every system resulting in from reaction functions it business will be 9 92-16. how find a ? anda? is 16? The equilibrium value results the n replacement of equilibrium quantities in inverse demand function and is equal to 36 monetary units Chow lind 36?) Substituting the value the value and the equilibrium quantiry quantity in the function profit of each a ( a busness it turns out that the profits of each business will be 7 = 77=512 monetary units 51 aqu (ii) If business form cartels the maximization problem of the cartel profits will be. Maux [m-[100-2(q)]9-4(q). From the first class Ereaty =0, it turns out will be 24 units (how find 24? every business will produces am=q = 12 Chow find Substituting the quantities produced in profit function of each business it turns out that the pot profit of each business will be m = 1m=576 There fore 12?1 units. monetary TOPIC 3rd An industry has two companies (1 and 2). The cost function of enterprise i is C (qi) = 4qi, i = 1.2. The inverse demand function of the industry is p = 100 - 2q, where p is the price and q is the total quantity produced [ie. the sum of the quantities produced by 1 and 2 (q=q1 + q2)]. (i) Calculate the equilibrium according to Cournot. At what price will it be sold product and what will be the profits of each company? (ii) Assume that the two companies decide to form a cartel and each agree to produce of the total amount of the cartel. Calculate the amount that maximizes the profits of the cartel as well as the profit of each business, assuming that both companies respect the terms of the partnership. (iii) Assume that (a) market conditions are expected to remain unchanged (no change is foreseen), (b) the quantity produced by each firm during a year is accurately disclosed to its competitor, but only at the end of it of the year, (c) if a business does not comply with the cartel agreement in the first year, then the other company never cooperates with it again after that year and therefore the companies decide independently on the quantity they will produce in each period. Assume that the interest rate is r = 5%. Do you believe? that the partnership is sustainable? (LCC) if a ea company doe does not agreement for a period then it will & produce the quantity resultion function if we replace the quantity produced by its competion is partnership (12 units). So the quantity that this will produce business will be 18 units. As profits of this business will be is = [100-2 (30)] *18-4-18=46648 how find 18 ? and how hind 30? We know that of the partnership is the relationship that determines the viability 7.-7 So in order for the par - partnership to be viable the M than 576-512 interest rate should is less 6.889. So if the interest rate is 5% 648-576 partnership is sustainable (LCC) if a ea company doe does not agreement for a period then it will & produce the quantity resultion function if we replace the quantity produced by its competion is partnership (12 units). So the quantity that this will produce business will be 18 units. As profits of this business will be is = [100-2 (30)] *18-4-18=46648 how find 18 ? and how hind 30? We know that of the partnership is the relationship that determines the viability 7.-7 So in order for the par - partnership to be viable the M than 576-512 interest rate should is less 6.889. So if the interest rate is 5% 648-576 partnership is sustainable (LCC) if a ea company doe does not agreement for a period then it will & produce the quantity resultion function if we replace the quantity produced by its competion is partnership (12 units). So the quantity that this will produce business will be 18 units. As profits of this business will be is = [100-2 (30)] *18-4-18=46648 how find 18 ? and how hind 30? We know that of the partnership is the relationship that determines the viability 7.-7 So in order for the par - partnership to be viable the M than 576-512 interest rate should is less 6.889. So if the interest rate is 5% 648-576 partnership is sustainable Answer 7 () Each T decides on the quantity it will produce independent of its competitor to maximize its profits. The problem of moximizing 1-11 company 6 the profits of 1-01- I will be: company 0a Max = [100-29 +9) 39-49 From the first order condition an avn AVTI we derive the reaction function 99, of company is = 24-92 2 " The problem of maximizing Max 1 = [100-2(9 +92)]92-492 the profits of 2 will be company Av we derive the reaction function of 2 is KEF company 92 = 24-9 2 70 Solving the follows that the equilliprium quantity Cournot that will produce every system resulting in from reaction functions it business will be 9 92-16. how find a ? anda? is 16? The equilibrium value results the n replacement of equilibrium quantities in inverse demand function and is equal to 36 monetary units Chow lind 36?) Substituting the value the value and the equilibrium quantiry quantity in the function profit of each a ( a busness it turns out that the profits of each business will be 7 = 77=512 monetary units 51 aqu (ii) If business form cartels the maximization problem of the cartel profits will be. Maux [m-[100-2(q)]9-4(q). From the first class Ereaty =0, it turns out will be 24 units (how find 24? every business will produces am=q = 12 Chow find Substituting the quantities produced in profit function of each business it turns out that the pot profit of each business will be m = 1m=576 There fore 12?1 units. monetary TOPIC 3rd An industry has two companies (1 and 2). The cost function of enterprise i is C (qi) = 4qi, i = 1.2. The inverse demand function of the industry is p = 100 - 2q, where p is the price and q is the total quantity produced [ie. the sum of the quantities produced by 1 and 2 (q=q1 + q2)]. (i) Calculate the equilibrium according to Cournot. At what price will it be sold product and what will be the profits of each company? (ii) Assume that the two companies decide to form a cartel and each agree to produce of the total amount of the cartel. Calculate the amount that maximizes the profits of the cartel as well as the profit of each business, assuming that both companies respect the terms of the partnership. (iii) Assume that (a) market conditions are expected to remain unchanged (no change is foreseen), (b) the quantity produced by each firm during a year is accurately disclosed to its competitor, but only at the end of it of the year, (c) if a business does not comply with the cartel agreement in the first year, then the other company never cooperates with it again after that year and therefore the companies decide independently on the quantity they will produce in each period. Assume that the interest rate is r = 5%. Do you believe? that the partnership is sustainable