Question

1. Use the following information for Problems 10-14:  A company produces and sells a product with a monthly demand estimated to be Q = 500 - 5P, where P is the selling price per unit in dollars. The fixed cost of production is $1,000 per month and the variable cost of production is $20 per unit.

   Price = __________ at the profit-maximizing quantity.

   	A.	$45
   	B.	$60
   	C.	$35
   	D.	$52
   	E.	None of the above

Answer 1

Answer) One of the major concept of economics is that for a firm,profit maximization happens at a point where marginal revenue is equal to marginal cost,in this case marginal cost is $20,to find marginal revenue we will differentiate total revenue with respect to quantity,so we have to find total revenue first as follows

• Total revenue=Price*Quantity
• Q=500-5P which gives us 5P=500-Q or P=100-Q/5
• Total revenue then becomes (100-Q/5)*Q=100Q-(Q^2)/5
• Marginal revenue=d(Total revenue)/d(Quantity)=d[100Q-(Q^2)/5]/d(Q)=100-2/5Q
• Now equating marginal revenue with marginal cost we get MR=MC or 100-2/5Q=20 or 2/5Q=100-20 whic gives us Q=400/2=200
• Now putting Q 's above value in Q=500-5P ,we get 200=500-5P,which gives us 5P=300 or P=$60

So at P=$60,Marginal revenue equals marginal cost,thus price is $60 at profit maximizing point and correct answer is option b)$60.

Answer is complete.Thank you!