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Question

Please hepl me with this homework, Thanks in advance. 

Suppose a business has a product demand function of:

P=100-0.01Q USD units

Total cost function of enterprise TC = 50 Q

a. Write an equation that represents total revenue, marginal revenue, and marginal cost

TR? MR? MC?

TR=P*Q =(100-0.01Q)Q =100Q-0.01Q2

MR=TR’q=(100Q-0.01Q2)’=100-0.02Q

MC= TC’q=50Q’=50

b. Determine the level of output that maximizes the firm’s profit

Q? To maximize profits. MR=MC

100-0.02Q=50 Q=2500

c. If a business is subject to tax t=10USD/unit of product, how much output and price should the business need to maximize profits?

MCt=MC+t =50+10=60

P,Q? MR=MCt

100-0.02Q =60 Q=2000, SUBSTITUTE Q into the demand curve equation

P=100-0.01Q =100-0.01*2000 =80

d. Determine product prices and quantities to maximize revenue for businesses.

P, Q? To maximize revenue: MR=0

MR=100-0.02Q=0

Q=5000 Substitute into the demand curve equation

P=100-0.01Q =100-0.01*5000 =50