A firm's technology is characterized by a Cobb - Douglas production function of the form 1 1 y = f(K.L) = 2K² + 1² a. The output price is p, and the input prices are r and w for K and L, respectively. Set up the problem for a profit - maximizing firm and solve for the factor demand functions for K and L. b. Find the firm's supply function. c. Find the firm's profit function. d. Assume

A firm has a cost function of C = 1000 + 20Q + 1/10Q2a) Estimate the firm’s demand function. You may assume that the slope is a wholenumber, and the intercept is a multiple of 10. b) Find the firm’s revenue function. You do not need to draw it. c) Find the marginal revenue function, and draw it on a copy of the graph. d) Find and draw the marginal cost function.e) Use your results from parts (c) and (d) to find the profit-maximising level of output.(3 marks)f) Find the market price at this level of output.

Problem 2.5    The cost function for Acme Laundry is  TC(q) = 10 + 10q + q^2 so its marginalprod cost function is  MC(q) = 10 + 2q where q is tons of laundry cleaned.  Derive the firm's average cost and average variable cost curves.  What q should the firm choose so as to maximize its profit if the market price is p?  How much does it produce if the competitive market price is p = 50?

A competitive firm's production function is given by y = f(K, L) = 8K 1/2 + L 1/4 Assume that the price of the good produced is p = $100, the price of capital is r = $4, and the price of labor is w = $5. Find the profit- maximizing levels of capital and labor (K * and L * ). Find the profit-maximizing level of output (y * ). What is the maximum profit of the firm (π * )?

The two side by side graphs are for two firms that between them supply all the original grown advocados for a local area. With vigorous competition between the firms, the price per pound has settled at a point where both firms are just breaking even. For each firm, the marginal cost (mc) average variable cost (avc) and average total (atc) curves are shown In the blank graph below, use the straight line tool to draw a straight line representing the short run market supply curve for quantities above zero. (that is Dont worry about operating points for which the quantity is zero)

In competitive markets, there are many small firms with each firm unable to influence the market price. Suppose company ABX  operates in the wheat market. The company produces and markets wheats at a Price = $20 per container. The firm’s total costs are given as: TC = 50 +2Q + 3Q2   What is the firm Fixed Cost? Why? Also, use a graph to support your answer

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Consider a firm with the following cost function:   C (q) = 4q^2 + 100   Find the long-run supply and the short-run supply of the firm, under the assumptions that the total cost function is the same in the long and in the short run, but the xed cost is sunk in the short run.

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_________.

3. A firm has a production function given by 1 1 A) y = 4x³x² ; 1 1 B) y = 3x4x² ; a) What are the factor demand functions? b) What are the conditional factor demand functions? c) What is the cost function? d) What is the supply function? 1 1 C) y = 5x³x2; 11 D) y = 12xx².