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Application of Differentiation
1. The demand equation for a manufacturer’s product is p = 20 - 0.25q, 0 q 80
where q is the number of units and p is the price per unit. At what value of q will there be maximum revenue? What is the maximum revenue?
2.The demand equation for a monopolist’s product is p = -5q + 30. At what price will revenue be maximized?
1.A manufacturer’s total cost function is given by c = q2/4 + 3q + 400
where c is the total cost of producing q units. At what level of output will average cost per unit be a minimum?
2.A manufacturer finds that the total cost c of producing a product is given by the cost function c = 0.05q2 + 5q + 500
At what level of output will average cost per unit be a minimum?
1. For Monopolist’s product, the demand function is p = 72 - 0.04q and the cost function is c = 500 + 30q. At what level of output will profit be maximized? At what price does this occur, and what is the profit?
2. For a monopolist’s product, the demand equation is p = 42 - 4q, and the average cost function is = 2 + 80/q. Find the profit maximizing price
3. Suppose that the demand equation for a monopolist’s product is p = 400 - 2q and the average cost function is = 0.2q+4+400/q, where q is number of units and both p and
are expressed in dollars per unit
a.Determine the level of output at which profit is maximized
b.Determine the price at which maximum profit occurs
c.Determine the maximum profit
% change in quantity
% change in price
1. When || > 1, demand is elastic
2. When || = 1, demand has unit elasticity
3. When || < 1, demand is inelastic
a. Find the point elasticity of demand for the demand function p = 1200 - q2 at q = 10.
b. Determine the point elasticity of demand equation q = p2 - 40p + 400 (where q > 0) at p = 15.
so 1 + 1/ > 0
total revenue increases if demand elastic
so 1 + 1/ < 0
total revenue decreases if demand