MICROECONOMICS
posted by Brett .
Hello ive been struggling with this problem for about 2 days now could someone walk me through it?
Suppose a firm faces a downward sloping demand curve given by the equation Q = 100  (1/3)P. The firm's cost function is given by the equation C = 30 + (1/4)Q^2. Find the Profit Maximizing level of output.
thank you

always always always, MC=MR.
First rearrange the demand function to be P=f(Q). That is P=33.33  Q/3
Now then Total revenue is P*Q. So TR=33.33Q (Q^2)/3
MR is the first derivitive of TR. So MR=33.33  (2/3)Q
MC is the first derivitive of TC. So MC=(1/2)Q
MC=MR  use algebra and solve for Q. Take it from here 
oops, my bad algebra. I divided by 3 instead of multiplying by 3. So, P should be P=300  3Q.
But follow the same methodology as before starting from here.
Respond to this Question
Similar Questions

Economic
Suppose that labor is the only input used by a perfectly competitive firm that can hire workers for $50 per day. The firm’s production function is as follows: Days of Labor/Units of Output: 0/0, 1/7, 2/13, 3/19, 4/25, 5/28, 6/29, … 
Economics
How can you obtain a downward sloping market demand curve from a horizontal firm demand curve experiencing perfect competition? 
Economics
Suppose a firm faces a downward sloping demand curve givven by the equation 1=1001/3P. The firm's cost function is given by the equation C=30+1/4Q^2. Find the profit maximizing level of output. 
econ
1. Consider a pure monopolist with shortrun total cost function given by STC = 1000 +200 Q + 12.5 Q2. Suppose also that this firm faces an inverse market demand function given by P = 800 – 20 Q. a. How much should this firm produce … 
Economics
n autoservice establishment has estimated its monthly cost function as follows: TC = 6000 + 10 Q where Q is the number of cars it services each months and TC represents its total cost. The firm is targeting 35,000 net monthly profit … 
microeconomics
Market demand is given as QD = 200 – 3P. Market supply is given as QS = 2P + 100. Each identical firm has MC = 0.5Q and ATC = 0.25Q. What quantity of output will a typical firm produce? 
Economics
got this from my teacher, A monopolist faces a demand curve given by the following equation: P = $500 − 10Q, where Q equals quantity sold per day. Its marginal cost curve is MC = $100 per day. Assume that the firm faces no fixed … 
microeconomics
Market demand is given as QD = 200 – 3P. Market supply is given as QS = 2P + 100. Each identical firm has MC = 0.5Q and ATC = 0.25Q. What quantity of output will a typical firm produce? 
Economics
A monopoly firm faces a demand curve given by the following equation: P = $500 − 10Q, where Q equals quantity sold per day. Its marginal cost curve is MC = $100 per day. Assume that the firm faces no fixed cost. You may wish … 
monoplistic competition
Suppose that a typical firm in a monopolistically competitive industry faces a demand curve given by: q = 60 − (1/2)p, where q is quantity sold per week. The firm’s marginal cost curve is given by: MC = 60. How much will the …