Microeconomics Homework

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.

Firm 1’s Profit = P*Q1 - C1*Q1 = 300*50 - 300*50 = 0
Firm 2’s Profit = P*Q2 - C2*Q2 = 300*50 - 300*50 = 0

Hence, due to the price war, both