Assume a firm is a small business and act as a price-taker in the market, the market price of the firm’s product is 20. The firm’s cost function is:
C(q) = 0.5q2+5q+100.
1. What is the firm’s optimal output level?
2. What’s the firm’s highest profit?
1. Optimal output level
Firm’s cost function is:
"C(q) = 0.5q^2+5q+100"
Under perfect competition, a firm is a price taker of its good since none of the firms can individually influence the price of the good.
To calculate the optimal level of output at which its;
Marginal Cost (MC) = Market Price (P)
"MC=\\frac{d(TC)}{dQ}"
"MC=\\frac{d(0.5q^2+5q+100)}{dQ}=q+5"
"MC=P"
"q+5=20"
"q=15"
2. Firm's profit
"Profit = Revenue - TC"
"Revenue =PQ=20\\times15=300"
"TC=0.5\\times(15)^2 +(5\\times15)+100=287.5"
"Profit = 300-287.5=12.5"
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