Solve Economics Questions: Quantity Produced by Woodard to Maximize the Profit (Math Problem Sample)

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* Marginal cost curve
Marginal cost curve= dTC /dQ
= -1000+200Q
* Woodard’s marginal revenue function
Marginal revenue function=dTR/ dQ
Total revenue=P*Q
TR= 30000*Q=30000Q
* quantity produced by Woodard to maximize the profit
Profit=TR-TC
TR=30000Q
TC=500,000 -1,000Q + 100Q2
Ï€=30000Q-(500,000 -1,000Q + 100Q2)
Ï€=31000Q-500000-100Q2
d π/dQ= 31000-200Q
200Q=31000
Quantity produced by Woodard=155
Profit=31000(155)-50000-100(1552) =$2,352,500
* If Woodard Inc. chooses the profit maximizing level of production for a monopolist, output they will they produce.
The monopolist's profit-maximizing level of output is found by equating its marginal revenue with its marginal cost,
MR=MC
TR= (40,000 - $20.50Q) Q
40000Q-20.50Q2
MR=40000-41Q
MC=-1000+200Q
40000-41Q=-1000+200Q
41000=241Q
Q=170
* Given the output calculated in part d, the price will they be able to charge as a monopolist
p=40,000 - $20.50Q=40,000-20.50(170)
Price=36515
* Given that the price was $30,000 before the other firm went out of business, and assuming that there was no unmet demand at this price, how much total production was occurring in the market? Now that there is only one firm, how much has consumption decreased?
TOTAL market demand curve was P = 40,000 - $20.50Q
Price$-30000
30000=40000-20.50Q
10000=20.50Q
Q=488
The total production was=488 units
Current production=170 units
Decrease in consumption=488-170=318 units
* What I can say about the relative costs of the firm that went out of business compared to Woodard Inc.
What I can say about the large firm that went out of business is that the firm was operating at the point where the marginal costs were more than the marginal revenue. This means that the firm was not in a position to maximize the profits and hence it operated in losses. The high-cost costs therefore led to the firm going out of business.
*
The consumer advocacy groups advocate for making use of the natural resources. On the other hand, the environmental conservation groups condemn the depletion of resources
Quantity demanded escalates among the consumers due to the consumer advocacy groups. On the other hand, quantity demanded decreases due to the environment conservation groups. Therefore the consumer advocacy groups increase the quantity demanded while environment conservancy group works towards decreasing the quantity demanded.
*
The firms were not acting as a cartel. This is because according to the industry, they were charging a price at which they would be able to maximize their profits without having to engage the price wars. The price that they were charging was at the point where the marginal cost equals the marginal revenue.
MR=MC
Price$-30000
30000=40000-20.50Q
10000=20.50Q
Q=488
The total production was=488 units
488 units comprised of the total units produced and there was no unmet demand at this point meaning that the companies were not acting as cartels.
Question 2
The profit maximizing price in each market
The following formula gives the relationship between the marginal revenue and the price elasticity
At maximum profit, marginal cost equals the marginal revenue
P- Profit maximizing price
n- Elasticity of price
Canadian sweaters=20*(-1.56/ (-1.56+1) =$56
Australian sweaters=15*(-3.62/ (-3.62+1) =$21