Economic Optimization Numerical
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This document contains sample optimization problems related to profit maximization for a firm. It includes questions about finding the profit-maximizing output level given total revenue and cost functions, the impact of subsidies, and the output level that maximizes total revenue. It also provides examples of determining the profit-maximizing level of output, average cost function, and minimum average cost given total cost functions, as well as finding the output level where average cost is minimized and the corresponding marginal cost.
Economic Optimization Numerical
- 1. OPTIMIZATION PROBLEMS (Managerial Economics: BBAN 302) Q1. ProfitmaximizingoutputwhenRevenue& Costfunctionsgiven Q2. Profitmaximizingoutput& PointelasticitywhenRevenue& Costfunctionsgiven
- 3. Q3. Profitmaximizingoutput& impactof subsidywhenDemand&CostFunctionsare given
- 4. Q4. Find the maximum profits ‘π’ for a firm, given total revenue R = 4000Q – 33Q2 and the total cost function C = 2Q3– 3Q2+ 400Q + 5000, assuming Q > 0. Profit function: π= R – C Π = (4000Q – 33Q2)– (2Q3– 3Q2+ 400Q + 5000) = -2Q3– 30Q2+ 3600Q – 5000 Taking the first derivative, set it equal to zero, and solving this for Q we get critical points.
- 5. Taking the second derivative we get Q5: From the total cost function TC = Q3–5Q2 + 60Q find (1) the average cost AC function (2) the critical value at which AC is minimized and (3) the minimum average cost. Q6: Given the total revenue R = 15Q – Q2 find the Average Revenue (AR), Marginal Revenue (MR) and the level of output Q that maximizes Total Revenue (TR). The output that maximize TR =7.5; AR when Q=7.5 is 15-7.5 = 7.5; MR when Q =7.5 is 15-2(7.5)=15-15 = 0
- 6. Ex. 7: A firm has the following total cost, C and demand function Q C = 1/3 Q3– 7Q2+ 111 Q + 50 and P = 100 – Q (1) Write down the total revenue function R in terms of Q (2) Formulate the total profit function Solution: (1) Price function P = 100 – Q Revenue = P x Q The revenue function is R = PQ = 100Q – Q2 (2) Profit function is Π = TR – TC functions = (100Q – Q2) – (1/3 Q3– 7Q2+ 111Q + 50) Π = -1/3 Q3+ 6Q2– Q – 50 Ex 8: From the total cost function TC = Q3– 5Q2 + 60Q find (1) the average cost AC function (2) the critical value at which ACis minimized and (3) the minimum average cost. Ex 9: Given the Total Cost Function C = 1/3Q3- 3Q2+ 9Q, find Q when Average Cost is minimum. Find also the Marginal Cost at the level of Q. Putting Q = 9/2 in MC equation we get MC at Q = 9/2 is = 9/4