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understanding perfectly competitive markets algebraically.

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Please see the attached. I need assistance in determine the following:

1. How can I tell what the profit maximizing level of output is?

2. The average cost per unit for producing the output identified in
part A?

3. What is the firm's profit or loss?

4. Is the firm operating in the long run or in the Short run. How would I know this.

How can I make these determinations based off of the attached?

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https://brainmass.com/economics/supply-and-demand/understanding-perfectly-competitive-markets-algebraically-262396

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1. Lawn mowing services are supplied by a host of individuals in the suburb of Westbrook. Demand and supply conditions in the perfectly competitive domestic for lawn mowing services are:
P = $75 - 1.75QD Demand
P = $2QS Supply
where P is price per lawn mowed and Q is quantity of lawns mowed per day.

a.) Algebraically determine the equilibrium industry price/output combination.
P = $75 - 1.75Qd Qd = (-P + 75) / 1.75 Qs = P / 2
Qd = (-P + 75) / 1.75 Qd = (-40 + 75) 1.75 Qs = 40 / 2
Qd = 35 / 1.75 Qs = 20
P = $2Qs Qd = 20
Qs = P / 2
Equilibrium Price = $40
Qs = Qd Equilibrium Quantity = 20
P / 2 = (-P +75) / 1.75
1.75P = (-P + 75) / 2
1.75P = (-2P + 150)
2P + 1.75P = 150
3.75P = 150
P = 150 / 3.75
P = $40

b.) Confirm this by graphing industry demand and supply curves (Using excel). For the graph, use prices: 10, 20, 30, 40, 50, 60, 70, 80, 90 and Quantities: 5, 10, ...

Solution Summary

The following outlines the process of algebraically solving for equilibrium and calculating a firms profit or loss.

$2.19