suppose that input prices are (w, r) >> 0 as before, and p > 0 is the price of the output good Y. (a) Formulate the firm's profit maximization problem.
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- 2. Suppose the production function of a firm is given by f (x₁, x2) = 2x₁ +4x2. (a) Calculate the conditional demand functions of the firm assuming w₁ = 2, W₂ = 3, and y = 8. (b) Calculate the minimum cost of the firm to produce 8 units of the good when w₁ = 2 and w2 = 3.Q.5 A firm is making two products A & B. Each unit of A incurs a cost of production to the tune of $150 and that of B incurs a cost of $200. Product A earns a profit of $15/unit and B gets $20/unit. The estimated monthly demand of both A & B is at maximum 500 units. Monthly production budget is set at $50,000.How many units of A & B should the firm make in order to maximize profit. Conduct sensitivity analysis and answer the following questions: 1. State the optimal solution. 2. What is the objective function value? 3. Find out the range of profit for A in the objective function for which the above solution remains optimal. 4. Which constraint/s is/are binding? 5. Interpret the shadow price for production budget.Suppose that total unit sales of iPhones and Android phones depends on both Apple’s and Google’s advertising expenditures: Google Advertise Don’t Apple Advertise 100, 100 120, 60 Don’t 60, 120 80, 80 To find the firm’s profits from the sales figures, assume that the price is $30, that the marginal cost is $20, and that the fixed cost of advertising is $300. (a) Fill in the profits in the following simultaneous-move game: Google Advertise Don’t Apple Advertise ? ? Don’t ? ? (b) What is the Nash equilibrium of the game? What strategies result in thehighest industry profits? Explain in words why the firms don’t choosethose strategies?
- On the graph input tool, change the number found in the Quantity Demanded field to determine the prices that correspond to the production of 0, 6, 12, 15, 18, 24, and 30 units of output. Calculate the total revenue for each of these production levels. Then, on the following graph, use the green points (triangle symbol) to plot the results. Calculate the total revenue if the firm produces 6 versus 5 units. Then, calculate the marginal revenue of the sixth unit produced. The marginal revenue of the sixth unit produced is________. Calculate the total revenue if the firm produces 12 versus 11 units. Then, calculate the marginal revenue of the 12th unit produced. The marginal revenue of the 12th unit produced is_________.1/3 1/3 Assume y = f(x1, x2) = x1 x2 . If the input prices are w₁ and w₂ what is profit maximizing y level of output? What is the profit?Prove it! 2. If the demand function for products A and B is in the order Pa = 36 - 3Qa and Pb = 40 - 5Qb and the common cost function is TC = Qa' + 2QaQb + 3Qb². With the above information, then calculate: a. Production values A and B at the maximum or minimum profit levels. b. The maximum or minimum profit value Did the profit reach its maximum or minimum value? Prove it c.
- 3. Suppose the production function of a firm is given by f (x1, x2) = min {x1, x2}. (a) Calculate the conditional demand functions of the firm assuming w₁ = 2, w2 = 4, and y = 8. (b) Calculate the minimum cost of the firm to produce 8 units of the good when w₁ = 2 and w2 = 4.A firm has the following demand function P=200-2Q and the average cost of AC=100/Q+3Q-20 a. Find the profit function. b. Estimate the marginal cost function. c. Obtain the production that maximizes the profit. d. Evaluate the average cost and the marginal cost at the maximising production level.cise 2[F] The profit function of a business firm is 1 3 T = f(q) = -³ + 6q² – 11q – 50. (i) What output q should the business firm produce to maximize the profit? (ii) What is the maximum profit the business fırm can generate?
- Suppose that a farm manager seeks to maximize its total profit function a s given by the equation, profit =80x-2x^2-xy-3y^2+100y. let x=cabbages and y= onions. but the manager faces a constrain that the sum of the cabbages and onions must be equal to 12.a. Calculate the level of output at which the farm maximizes profitb. Calculate the farms profit.13. The marginal profit for the new X-99 pogo stick is P'(x) = -0.1x+ 60 where x is the number of sticks produced and sold. The profit is - $1000 when 50 sticks have been produce and sold. a) Find the profit function. b) What level of production of pogo sticks (x) produces a maximum profit?True or false: Profit is the difference between the total revenue generated and cost of goods sold. True or False?
