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## Matematika ekonomi

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**Derivatives of Logarithmic Functions**• Find dy/dx 1. 2. 3. 4.**Derivatives of Exponential Functions**Find dy/dx 1. 2. 3.**Applied Maxima and Minima**• Maximizing Revenue • Minimizing Average Cost • Profit Maximization • Elasticity of Demand**Maximizing Revenue**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?**Minimizing Average Cost**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?**TUGAS**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**Profit Maximization**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**Elasticity of Demand**• Economists measure how a change in the price of a product will affect the quantity demanded • The ratio of the resulting percentage change in quantity demanded to a given percentage change in price: % change in quantity % change in price**Continue …...**• If p = f(q) is a differentiable demand function, the point elasticity of demand denoted by:**Continue …...**1. When || > 1, demand is elastic 2. When || = 1, demand has unit elasticity 3. When || < 1, demand is inelastic**Continue …...**• Example 1 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.**Continue …...**• If demand is elastic, then < -1, so 1 + 1/ > 0 total revenue increases if demand elastic • If demand is inelastic, then > -1, so 1 + 1/ < 0 total revenue decreases if demand inelastic

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