Problem 1: C(Q) = 100 + 20Q + 15Q^2 + 10Q^3 a) Fixed Cost (doesn’t change depending on output produced) = 100 b) Variable Cost of producing Q = 10 units: 20*10 + 15*10^2 + 10*10^3 = 200 + 1,500 + 10,000 = 11,700 c) Total Cost of producing Q = 10 units: C(10) = 100 + 20*10 + 15*10^2 + 10*10^3 = 11,800 Alternatively, we have Total Costs of Producing Q=10 units = Fixed Costs + Variable Costs of producing Q = 10 units = 100 + 11,700 = 11,800 d) Average Fixed Cost = Total Fixed Costs / Output = 100/10 = 10 e) Average Variable Cost = Total Variable Costs of producing Q= 10 units / Output = 11,700/10 = 1,170 f) Average Total Cost = Total Costs of producing Q=10 units /…show more content… The equations are stated below. Assume Firm 1 is the leader. Q1 = (a + c2 -2c1)/2b = 300/6 = 50 Q2 = (a - c2)/2b - Q1/2 = 50 - 50/2 = 25 Here we see that Firm 1 being the leader has an output of 50 which the other firm follows and reaches equilibrium by producing a much lesser output of 25
Price = 600 - 150 - 75 = 375 Profit_1stFirm = (P - c1)*Q1 = 75*50 = $3750 Profit_2ndFirm = (P - c2)*Q2 = 75*25 = $1875 Firm 1 makes a profit much greater than that of firm 2 in the stackelberg model!
The output and profits of firm 1 by this model are greater than that of firm 1 by the cournot model. This is so, because by moving in first, firm 1 is able to capture a larger market share and hence a greater profit!
Bertrand Model:-
Due to a price war, both the firms keep undercutting and this results in a situation such that the equilibrium price settles down at a level equal to the Marginal Cost of the product.
Therefore P = 600 - 3Q1 - 3Q2 = MC = 300 3(Q1 + Q2) = 300 Q1 + Q2 = 100 Assuming that the market is equally distributed, Q1=Q2 Hence, Q1 = Q2 = 50
Due to the price war which leads to low prices, the demand increases, causing firms to produce more than that in the cournot model and the Stackelberg Model.
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