Suppose the marginal cost of producing diamonds is a constant$1,000 per diamond

Question

Suppose the marginal cost of producing diamonds is a constant$1,000 per diamond and demand is described by the following schedule: Price Quantity $8,000 5,000 diamonds 7,000 6,000 6,000 7,000 5,000 8,000 4,000 9,000 3,000 10,000 2,000 11,000 1,000 12,000 a. If there were many suppliers of diamonds what would be theprice and quantity? b. If there were only one supplier of diamonds what would bethe price and quantity? c. If Russia and South Africa formed a cartel what would bethe price and quantity? If the countries split the market evenly, what would be SouthAfrica’s production and profit? What would happen to South Africa’s profitif it increased its production by 1,000 while Russia sticks to the cartelagreement? d. Use your answer in part c to explain why cartel agreementsare often not successful. Suppose the marginal cost of producing diamonds is a constant$1,000 per diamond and demand is described by the following schedule: Price Quantity $8,000 5,000 diamonds 7,000 6,000 6,000 7,000 5,000 8,000 4,000 9,000 3,000 10,000 2,000 11,000 1,000 12,000 a. If there were many suppliers of diamonds what would be theprice and quantity? b. If there were only one supplier of diamonds what would bethe price and quantity? c. If Russia and South Africa formed a cartel what would bethe price and quantity? If the countries split the market evenly, what would be SouthAfrica’s production and profit? What would happen to South Africa’s profitif it increased its production by 1,000 while Russia sticks to the cartelagreement? d. Use your answer in part c to explain why cartel agreementsare often not successful. d. Use your answer in part c to explain why cartel agreementsare often not successful.

Explanation / Answer

According to the demand schedule, Price per diamond = 13000 -Quantity of diamonds a. Assuming perfect competition, long run equilibrium Price =Marginal Cost = $1000     and Quantity = 13000 - Price = 12000diamonds b. Monopoly chooses Price and maximizes profit function subject tothe Demand Schedule Quantity = 13000 - Price:     Profit = (Price - Marginal Cost)*(Quantity) =(Price - 1000)*(13000 - Price)     First Order Condition Yields: 14000 - 2*(Price)= 0     Solve for Price: Price = 7000 and Quantity =13000 - Price = 6000 c. A cartel, if successful, acts as a monopoly, setting price andtotal quantity to the monopoly levels above. The resulting profitis split by the members of the cartel:        Total Profit = (Price - MarginalCost)*(Quantity) = (7000 - 1000)*(6000) = 36000000     So South Africa would receive a profit of36000000/2 = 18000000 if the cartel splits the market evenly, eachproducing supplying 3000 diamonds so that the equilibrium price isPrice = 13000 - Total Quantity = 13000 - 2*3000 = 7000.     Assuming Russia sticks to the agreement andsupplies 3000, if South Africa increases production to 4000, thenthe resulting Price according to the demand schedule should bePrice = 13000 - Total Quantity = 13000 - (3000 + 4000) = 6000 andSouth Africa's individual profit increases to Profit = (Price -Marginal Cost)*(South Africa's Quantity) = (6000 - 1000)*(4000) =20000000>18000000 under the agreement of the cartel. d. Part c shows how each member of the cartel has an incentive todeviate from the agreement and, as a result, over produce, earninga higher profit than they would under the agreement assuming thatthe other member of the cartel sticks to the agreement. As aresult, no member is willing to trust that the other member willstick with the agreement and the cartel breaks down since it cannotbe sustained as a Nash Equilibrium.

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